The Features of a type are specifically features of racial hit dice for creatures of that type. Since the alienist (presumably) has no racial hit dice, none of those apply.
So that means no change in HP, BAB, or skill points.
The Traits, on the other hand, do, so the alienist gets all of those (and loses the Traits of his or her previous type).
Moreover, despite the definition of Outsider (native), you only get the native subtype if the thing says you get it, and alienist doesn’t (because you have become so alien that you no longer count as native).
So that means darkvision, simple and martial weapon proficiency, and yes, both difficulties being resurrected and no need to eat or sleep.
Based off of DDAL1 modules...
The Table:
\begin{array}{l c l}
\text{Total GP Expended} & \text{Level} & \text{(Expenditure for next level)} \\ \hline
0 & 1 & (700) \\
700 & 2 & (1,000) \\
1,700 & 3 & (1,350) \\
3,050 & 4 & (1,850) \\
4,900 & 5 & (2,500) \\
7,400 & 6 & (3,500) \\
10,900 & 7 & (4,750) \\
15,650 & 8 & (6,500) \\
22,150 & 9 & (8,750) \\
30,900 & 10 & (12,000) \\
42,900 & 11 & (16,500) \\
59,400 & 12 & (22,500) \\
81,900 & 13 & (31,000) \\
112,900 & 14 & (42,500) \\
155,400 & 15 & (58,000) \\
213,400 & 16 & \\
\end{array}
The Method:
I went ahead and tabulated the possible XP to earn and possible treasure haul2 for each of the two-dozen or so DDAL modules I've got on hand.
Each module is designed for one of the following level spans3: 1-2, 1-4, 5-10, or 11-16.
From the XP earned in each I calculated a fraction of the indicated level span that would be "traversed" by completing the module, and used that to extrapolate how much gold would accrue to one gaining a level in that span.
I then weighted each by the recommended hours of play4 and ran a power regression.5.
Finally there's just a bit of rounding to make the numbers... round.
The Application:
Full confession: I don't think this ^^ is the best way to come up with these numbers.6 But I think it's a way and figured it's worth letting voters see so that wiser heads than mine can decide.
Those numbers are just... insane. Dropping that much cash--per adventurer!--onto the population of Barovia is just ridiculous. I know that D&D doesn't try to model any sort of functioning economy, but this is a bridge too far for my credulity. So you've got to find ways to ameliorate it. Perhaps use this table as a party table, so that once PCs have dropped 700gp everyone bumps to level 2? Perhaps adapt Delta's advice and switch to a silver standard (for XP) so that this all drops by an order of magnitude? Or perhaps...
magical items should be allowed as part of this scheme. Buying everyone a round and carousing for a night doesn't feel (to me) very different from rescuing a villager from weres and tossing a potion of healing their way. But this could also be a place where you can exert a GM's thumb on the scale, since the "values" of any items that the players disposed of in a way that buffed their renown aren't terribly standard. (And to that end, I'd recommend the Sane Magic Item Prices index; it may not be perfect, but it's waaay better than following the DMG's loose guidelines.) And now you've given players the interesting choice between hanging onto their widget of frobbing or "cashing it in" to level up. (Or level everyone up, per point 2!)
1 - Dungeons & Dragons Adventurers League, WotC's organized play program that was (and sort-of is?) active during 5e. The modules published through this program followed a rough set of guidelines for XP and treasure given out, and I'm using this as an insight into what WotC employees (Chris Tulach, specifically, perhaps with input from other designers?) thought was a good pacing of treasure accumulation by level.
2 - only coinage; since you indicate your players won't really be able to "cash in" any magical items, we're going strictly off of currency here. But more on this later.
3 - I'm using the term "span" rather than "tier" as "tier" is a defined term in 5e (PHB p.15) and these modules don't all correspond to tiers. It feels clunky, but I didn't want to conflate the ideas.
4 - Some modules--only in the lowest two spans--are recommended for two hours, most are recommended for four. This then has the effect of dialing back the impact of these smaller modules. However, there are many more of them (fifteen in 1-2 and 1-4) than in the higher levels (six in 5-10, one in 11-16) so the model's still drawing more of its info from those levels.
This weighting toward low-level information strikes me as fine in one way, as that's where the majority of play tends to happen. On the other hand, this means that any "errors" in the model are likely to appear at the high end, where it's going to take a while for you to notice and be really hard for you to fix: "oh, dear, we've been on level 10 for five sessions now, and are only halfway through. And I want them at 12 to face Strahd et al. for the last time and there's almost nothing left to explore!"
5 - power regression based on eyeballing this curve.
6 - I can think of one better way, but it's going to have to wait until I get my copy of CoS back from a buddy.
Best Answer
Ignore the level loss. It was a bad idea to begin with.
D&D 3.5e handles split-level parties extremely poorly. The power gained in a single level can be unbelievably immense (typically, when a new spell level is gained), which makes producing challenges that each character can reasonably contribute to without any dominating near-impossible depending on who is over-leveled. It doesn’t add anything to the game—if the player was invested in their character, then the character’s death is already loss enough, you don’t need more. And if they weren’t, well, then, it’s a good thing they’re playing a different one, because you want your players invested in their characters (I mean, usually, most tables, though of course it’s possible to play D&D like Paranoia).
As for resurrection and true resurrection, it’s not true that their only benefits center on level loss: their primary benefit is that they can resurrect creatures that weaker spells cannot. Resurrection needs only the smallest part of the target’s body, and true resurrection doesn’t even need that. Raise dead requires a mostly-intact corpse. A body that has been formerly raised as the undead cannot be raised by raise dead, but can by resurrection and true resurrection. True resurrection can also raise elementals and outsiders. And raise dead can only raise targets who have died in the last CL days, while resurrection or true resurrection can handle up to 10×CL years.