To infuse an item, you need the nonmagical version of that item.
The artificer's Infuse Item feature states (TCoE p. 12, E:RftLW p. 57, WGtE p. 179; emphasis mine):
At 2nd level, you gain the ability to imbue mundane items with
certain magical infusions. [...] Whenever you finish a long rest, you
can touch a non-magical object and imbue it with one of your
artificer infusions, turning it into a magic item. An infusion works
on only certain kinds of objects, as specified in the infusion’s
description.
The Artificer Infusions section at the end of the class description states (TCoE p. 20, E:RftLW p. 61, WGtE p. 181; emphasis mine):
The description of each of the following infusions details the type
of item that can receive it, along with whether the resulting magic
item requires attunement.
And finally, the description of the Replicate Magic Item infusion states (TCoE p. 22, E:RftLW p. 63, WGtE p. 182; emphasis mine):
[...] Alternatively, you can choose the magic item from among the
common magic items in the game, not including potions or scrolls.
In the tables, an item’s entry tells you whether the item requires
attunement. See the item’s description in the Dungeon Master’s Guide
for more information about it, including the type of object required
for its making.
Each of these portions I've bolded make it clear that you need a nonmagical version of the item to infuse, whether you're using Replicate Magic Item or one of the other artificer infusions.
Even though the Dungeon Master's Guide doesn't actually say "[X] is the type of item needed to make [Y]" for any listed magic item (as far as I know), this sentence seems to refer to the fact that each magic item that can be replicated is essentially an enhanced version of a clearly identifiable mundane item.
For instance, boots of elvenkind are boots, so the clear implication is that you would need mundane boots to infuse if you want to use Replicable Magic Item to make boots of elvenkind. This follows the same logic as the Boots of the Winding Path infusion (TCoE p. 21, E:RftLW p. 62, WGtE p. 181), which does explicitly state:
Item: A pair of boots [...]
In the case of your example, the description of cast-off armor states (XGtE, p. 136; emphasis mine):
Armor (light, medium, or heavy), common
Thus, you need a nonmagical version of whatever kind of armor you want to turn into cast-off armor. If you want cast-off half plate armor, you need a nonmagical set of half plate armor to imbue with that infusion.
The Replicate Magic Item infusion doesn't create a magic item from thin air - it gives you the ability to imbue a certain mundane version of that item with the necessary magic to function as that magic item.
Prosthetic limbs no longer require attunement
The November 2020 errata for Eberron updates the item description:
This item’s attunement requirement has been removed, and both paragraphs of the item’s description have been replaced with the following text: “This item replaces a lost limb—a hand, an arm, a foot, a leg, or a similar body part. While the prosthetic is attached, it functions identically to the part it replaces. You can detach or reattach it as an action, and it can’t be removed against your will. It detaches if you die.
Without attunement, there is no longer any interaction with Soul of Artifice to add bonuses to your saving throws.
Below is the original answer which I am going to keep due to the previous voting. But please see above for the current answer that includes the November 2020 Errata for Eberron.
Those magic items don't change the attunement values.
You've quoted all the relevant bits, but the key aspect here is also what you've said: that the 'grouped' attunements count as a single attunement, and it is the attuned magic items that count towards the capstone feature.
Prosthetic Limb
This counts as a magic item attunement. If you've got multiple prosthetic limbs, they still just count as a single attunement.
So no matter how many limbs you've got, you're just using up one attunement slot and generating a +1 bonus because the rules state they count as one.
Wand Sheath
The Sheath has similar wording as to the limbs, in that sheath and wand count as a single magical item for attunement, and therefore a single magic item with regard to the Artificer capstone.
But what about the fact that you've got multiple items? Shouldn't that increase the bonus?
Well, no, not really. I mean, the language is kind of loose, but the capstone refers to magic items attuned, not magic items total. And when each item like the prosthetic limb or wand sheath specifically states that they count as a single attunement, then it really is just that.
Best Answer
The Infusion class feature refers to specific infusion descriptions to declare what mundane objects can be infused, but the Replicate Magic Item infusion option doesn't appear to specify - all the other infusions have it immediately under the title. With that in mind, we're going to have to fall back on judgement calls - there doesn't appear to be a clear answer in the text.
It's reasonable to assume that the Replicate Magic Item feature requires a mundane version of whatever magic item you're making. With many magic items, this is perfectly clear - they're a weapon, a cloak or a jug.
The two items you asked about are referred to in their descriptions as a "prosthetic limb" and "prosthetic appendage."
I would rule that a mundane prosthetic is required - for example, a Prosthetic Limb infusion could turn the stereotypical pirate's peg leg and hook hand into a flexible leg and hand that work just like the user's original appendages.
I definitely wouldn't default to using a flesh and blood limb, as the items are described as prosthetics rather than reattached mundane limbs - it might be possible for a player to find a situation where this would make sense, but that feels like an exception to me.
Getting deeper into judgement calls, I think I'd say that the important point is that a mundane prosthetic can be attached to the appropriate part of the body, and this is what's required for the base item. I would also allow these as a relatively simple application of an appropriate artisan's tool proficiency, and it would be appropriate to make that easier if appropriate materials already exist - it's easier to make a prosthetic hand from a gauntlet, as those are already designed to attach firmly to an arm.
I would not allow an artificer to infuse some scrap metal and gears, as these aren't a mundane version of a prosthetic limb; but I would allow an artificer with scrap metal and gears to use their proficiency with Tinkerer's Tools to fashion a prosthetic limb, and then infuse that. The main differences here are that building the limb would take time and may call for an ability check, but also that it will remain in place even if the infusion ends for some reason; it's still a mundane prosthetic limb, whose function is to stay attached to the body and help the user move - it just won't be magically articulated any more.
Since mundane prosthetics are not (to my knowledge) addressed directly in the text of any rulebooks, working out appropriate time and costs for building one is also down to GM judgement, and may depend on how common you envision them being in the setting.