I'm using this mod with Q2XP (https://www.moddb.com/mods/quake-2-xp)

When I get into the start map with the teleporters and while playing the game I see three warnings on the top left:

Can't find pic: /players/male/sniper_i.pcx_bump
Can't find pic: bh100_bump
Can't find pic: ba0_bump

I'm not quite sure if this is a coopordie or q2xp issue. The first file has a sniper_i.pcx in the \baseq2\players\male\ directory and the last two files have a ba0.pcx and bh100.pcx in the \coopordie\pics\ directory.

I've tried making copies of bh100.pcx, ba0.pcx and sniper_i.pcx in their respective directories and renaming them to the expected names but this does not remove the errors.

Quake 2 XP console log:
https://zerobin.net/?73674c4f7808db75#H ... MQMuFreJw=

Hey, "sniper_i.pcx" seems like your skin's icon to me. It shows up in Coopordie's HUD (opened by default by pressing X). Maybe your skin doesn't have an icon (for example, use "skin male/grunt" in your console to change your skin and see the Grunt's icon instead - the error should no longer appear).

As for bh100.pcx and ba0.pcx, those come with Coopordie. They're the health and armor bars. You might need to redownload Coopordie's files here and make sure that coopordie/pics/bh100.pcx exists in your Q2 folder (aswell as the other file).

Now it just says that it can't find grunt_i.pcx_bump on the top along with the other two files.

I've already re-installed the mod.

I also mentioned in the OP that the files exist and in what folder they exist.

True.

I haven't seen this error before, so I assume it's due to Q2XP.

Try running vanilla q2 and see if the error still appears. If not, it must occur exclusively on Q2XP and you may probably find a solution by asking in their discord server.