dnd-5eresurrectionsoul
On DMG page 24, under "Bringing Back the Dead", it states:
A soul knows the name, alignment, and patron deity (if any) of the character attempting to revive it and might refuse to return on that basis.
I interpret the Warrior of the Gods (hereafter WoG) description as referring explicitly to the resurrection portion of the spell, and not necessarily the fact that the spell does additional things. I interpret WoG this way since Raise Dead is used as the example. Raise Dead has additional effects, but we can reason that it does qualify for the cost exemption since it's included as the example. Therefore, those additional effects must not matter to WoG, so the only thing left that must matter is the resurrection itself.
Clone does additional things, too (creating the body, in this case), but that is not what disqualifies it. Clone doesn't qualify for the cost exemption since it transfers the creature's soul into a new body, rather than actually resurrecting it. This is backed up by the answer to the question you linked in your comment.
This leaves us with 4 spells upon which we can focus: Revivify, Reincarnate, Resurrection, and True Resurrection.
Nota Bene: There is also one more spell that is capable of returning a creature to life: Wish. If we were concerned about material costs for Wish (which we aren't), we would treat Wish similarly to how I describe True Resurrection below. Whether or not this spell would qualify for a cost exemption would rely solely on the contents of the wish in question, and not the description of the spell, per my interpretation above. However, this ultimately doesn't matter, since Wish does not require material components to cast.
That said, let us examine the 4 remaining spells in our list:
Revivify's description reads:
You touch a creature that has died within the last minute. That creature returns to life with 1 hit point. This spell can't return to life a creature that has died of old age, nor can it restore any missing body parts.
This is straightforward enough that we can soundly reason that this spell qualifies for the exemption.
This spell comes with strings attached (emphasis mine):
You touch a dead humanoid or a piece of a dead humanoid. Provided that the creature has been dead no longer than 10 days, the spell forms a new adult body for it and then calls the soul to enter that body. If the target's soul isn't free or willing to do so, the spell fails.
The magic fashions a new body for the creature to inhabit...
This spell reads similarly enough to Clone that we can consider this spell to not qualify for the exemption. We are forming a new body here, as we did with Clone.
The Resurrection spell reads similarly to Raise Dead:
You touch a dead creature that has been dead for no more than a century, that didn't die of old age, and that isn't undead. If its soul is free and willing, the target returns to life with all its hit points.
This spell neutralizes any poisons and cures normal diseases afflicting the creature when it died. It doesn't, however, remove magical diseases, curses, and the like; if such effects aren't removed prior to casting the spell, they afflict the target on its return to life.
This spell closes all mortal wounds and restores any missing body parts.
Coming back from the dead is an ordeal. The target takes a −4 penalty to all attack rolls, saving throws, and ability checks. Every time the target finishes a long rest, the penalty is reduced by 1 until it disappears....
If we can reason from the WoG description that Raise Dead works as written, we can also reason that Resurrection should qualify. The important difference between the spells is the effective timeframe.
True Resurrection blurs the line between Clone and Raise Dead (emphasis mine):
You touch a creature that has been dead for no longer than 200 years and that died for any reason except old age. If the creature's soul is free and willing, the creature is restored to life with all its hit points.
This spell closes all wounds, neutralizes any poison, cures all diseases, and lifts any curses affecting the creature when it died. The spell replaces damaged or missing organs and limbs. If the creature was undead, it is restored to its non-undead form.
The spell can even provide a new body if the original no longer exists, in which case you must speak the creature's name. The creature then appears in an unoccupied space you choose within 10 feet of you.
By my aforementioned interpretation of WoG, this spell will qualify for the exemption only if it is not used to create a new body. If the spell is used to create a new body, we are now in Clone territory, and thus no longer qualify for the cost exemption.
In summation, we can comfortably say that Raise Dead, Revivify, and Resurrection all soundly qualify for the cost exemption offered by WoG. True Resurrection may or may not qualify, depending on how the spell is used.
There are a number of issues with this, but I'd say it's simply too strong, and I think some of the other issues needs to be addressed. I compare to "Dark One’s Blessing" because a lot of the features are of similar mechanics.
This is strong.
Next thing is that with impelling shroud you start with the hit points, where as with Dark One’s Blessing you have to kill something first, so that one needs multiple enemies to be as effective.
With Dark One’s Blessing you need to be the one dealing the killing blow to even get it. All of this combined makes impelling shroud much stronger.
This one is what I would consider the worst designed feature and I suspect that you care too much for the positives to realize all of the negatives.
Lastly, and this is important. The design is somewhat broken. You have added a price (Sacrifizing a creature that's goodish). The issue with the price is that for some characters that wouldn't even be a price at all. Now I know you say it's a big price for your players, but that doesn't make it much better. This is like saying: "Either you go against your characters wishes or you won't get to use this at all".
So either it's directly useless, which feels bad as a player or it's insanely overpowered, which feels bad for everyone.
I know it's meant as a "last resort" to your player, but you need to find a price that's equal to most characters and feels like an extreme price to pay, but not one you will feel bad about and not one that does specifically against the personality of the character/party.
Not much to say. This one is fine, but I would suggest removing it to make room for the reworked version of Sacrificial Virtue.
I like your fluff, but I have no idea how this makes me feel like an evil character sowing fear among my allies. I'd feel like a good guy buffing most of my party.
This is poorly designed. I like the execute effect, but it has insane synergy with Sacrificial Virtue. With that many D6 worth of damage and this ability, there's a fair chance you'd one-shot even some level appropriate enemies that are meant to be a challenge for the entire party.
The design problem comes from your own words: "Potentially quite powerful but very specific in its use", this is bad. If something is powerful and fun, I want to use it! Abilities like these will go one of two ways:
In some combats they will dominate, which won't feel good either.
Compare it to Hurl Through Hell. Hurl Through Hell is obviously stronger when it happens, but it's also "specific in its use", that specific being once a day. That is much better. That way the player will get to use it regularly and it won't suddenly pop multiple times during one encounter.
I'd suggest turning it into some kind of once-per-long-rest ability, as this gives the player much more agency. Maybe something that can only be activated when someone else thinks you are friendly to them (As means of assassination)
I would suggest moving some things around, nerfing the class generally and making it focus a little more on utility. This could be utility that helps isolate and kill targets.
This class takes too much agency away from the players and gives too much power. I think there are some really cool ideas, so I think you should keep working on it! This is definitely a cool start.
Best Answer
There Is No Rule
So it falls under a setting trope, but we'll come back to that.
In your first case, the character will return in the presence of the one doing the raising:
If the setting doesn't allow them to remember who brought them back, the caster in question will be close at hand to ask post-death.
In The Forgotten Realms...
A dead person becomes a petitioner. Until scooped up by their patron deity and brought to that deity's home plane, they are mindless beings. Even after reaching their patron's home plane, most petitioners remain mindless. Often, they're not even the same manner of creature as when they were alive - for example, many petitioners of The Triad eventually become lantern archons post-death.
So, in the Forgotten Realms, I'd say anything that happens while on the Fugue Plane or beyond (including attempts to resurrect) are not remembered when the recently dead ceases to be dead. Of course, how a mindless entity makes a decisions on who can raise them is a different (and unanswered) question.
In Other Settings
If you're not using a published setting, this is something you'd have to determine on your own. Unfortunately, there is no 5E source that covers it. Based on the releases to date, I don't expect there to be one. Your best bet to dig for ideas on how death works is probably 3E's Deities and Demigods.