Xbox less responsive and can't load games (0x8027025a)

Hi there, the performance of my Xbox One (bought on day one in 2013) has been slowly degrading for a while now and I'm not sure what to try next. It started out being unable to play larger games, for example in Battlefront 2 it either didn't load the game
at all or would take a few minutes to load in some textures which made the game unplayable, and after this happened the console would begin to lag in the menus constantly. This issue appeared a few times and I fixed with a mix of offline software updates and
factory resets which would solve the lagginess and older games were fine but newer games would still never run.

Today I was trying to play Lego Marvel Superheroes 2 and it initially wouldn't load, did load eventually but then was unable to swap characters or leave the first area loaded, just going black. I tried another factory reset (full, not keeping apps and user
data) but then the game wouldn't load, giving the error code 0x8027025a. After this didn't work, I tried yet another factory reset and now the game won't even install, getting stuck at 25%. I have managed to load and play the original 2005 Battlefront 2 though,
I just tested that to see if a very small game would work and it did.

Having gone through multiple factory resets I can't really see what else I can do at this point. My guess is maybe a faulty HDD is responsible which is why smaller games work but it still seems weird to me that for so long a factory reset was able to just
sort out the lagginess and have games run fine. Does anyone have any suggestions of what I could try and do to fix it now? I don't want to have to buy a new console this close to the release of the new generation.

:)