How likely is this the slave cylinder?

Audi a3 1.9tdi 2005 5 speed manual. Got it as a cheap banger, noticed sometimes it wouldn’t fully engage when putting it into reverse and would just make a grinding noise until I put it into neutral and tried again. Few months ago now I’ve noticed how it wouldn’t want to go into gear, sometimes only and it would only happen when going from second to third and from third to fourth.

Around three days ago now my mum borrowed the car to go to the shops and it broke down in the retail park, luckily she was able to park it up. Had my friend who fixes cars on the side check it out and he was able to drive it back home but said that it was awkward to do so, and reckons it’s the slave cylinder but isn’t 100% sure and said that it might still not work as it could potentially be something else. Picked up a new slave cylinder this morning and brake fluid and he said that he’ll be sorting it in a bit,

But now I’m just looking for a bit of peace of mind and you guy’s opinions, does this sound like the slave cylinder to you?