There are two main things that led me to this question: 1) I've never seen a squirrel in the Commonwealth, and 2) I learned that some meat sources are intentionally mislabeled (see Longneck Lukowski's Cannery, Doc Morbid, or Iguana Bob Frazier for more information).
Investigating squirrel meat in the Commonwealth and the Fallout Universe, I viewed the Fandom pages for Squirrel Bits (Fallout 4), Crispy Squirrel Bits (Fallout 4), Squirrel Stew, Crispy Squirrel Bits (general), Squirrel on a Stick, and finally, Squirrel.
One note from the Squirrel Stew page says:
Its commonality is strange as there are no squirrels to be found in the wastes, aside from those in Appalachia.
Another note, this one from Crispy Squirrel Bits (general), says:
Living squirrels can only be found in Fallout 76, yet there are still crispy squirrel bits in several of the games.
From the same page:
Crispy squirrel bits are squirrel kebabs that can be found in refrigerators or purchased from merchants. Another variety is found in the Commonwealth, which are cut up squirrel bits.
At first I took the second sentence to mean that it was indeed squirrel meat, but after considering, it is possible that the difference only denotes the format in which the meat is presented and not the veracity of its source.
Regarding the Squirrel on a Stick:
Squirrel on a stick is a common staple food eaten by denizens of the wasteland, made by ramming a stick through a squirrel and roasting it over an open fire, camping style.
The good news here is that squirrels, despite their lack of appearance in the Commonwealth, do canonically exist. However, the "on a stick" variant is the only one that I am confident in it actually being squirrel meat.
Do squirrel bits actually come from squirrels, or do they come from a more nefarious source?