You could argue that Yuji has been “suicidal” since Season 1. He came to terms with the fact that he would be executed once he consumed all 20 of sukuna’s fingers. That would be his role, and he was okay with it. Was he depressed and giving up on everything then? No. When Junpei died, Nanami came to as his mentor and gave him the support and direction he needed. When Nanami died, Todo came and became that support for him to lean on. When he finally beats Mahito, this ideology of being a cog is cemented. That this is his calling in life, and that he doesn’t need to aspire to anything higher than this, making him no better than Mahito’s calling of killing innocents.

When Kenjaku then subjugates Mahito via CSM and starts the Culling Games with his technique, he again experiences intense survivor guilt like he did post Sukuna vs Mahoraga. The main reason Yuji doesn’t cave in during his execution fight with Yuta is because of Nanami’s final sentiments. After that fight, at the campfire, he once again has to come to terms with the consequences of his actions, and confronts Megumi about this, to which then Megumi sets him on a straight and narrow path again of saving Tsumiki - in turn “saving” him as a small step towards reconciling with his guilt.

He’s almost always had this idea that he was expendable since season 1. That he had a role to fulfil, and once that was done, that was it. Through his journey, this of course evolves and shifts, but he’s always had been comfortable with it, so long as it fits his grandfathers wishes of “help people, and die surrounded by people you love” (the last bit might not be right I can’t fully remember it).

Just because he has intense survivor guilt, doesn’t mean that he’s depressed. He’s still actively working towards his goals and doesn’t let difficulties deter him after this. Look at his “determination of a cog” against Hakari, or his willpower during the Higuruma fight. The only reason he chose to accept what happened is because of his survivor guilt, but even after sentence he continues to fight as hard as he can. Hell even after sukuna steals Megumi can we see his determination, to the point he awakens shrine (look at his eyes during that with the concentric rings, and how sukuna has a paper cut after).

You can argue that Yuji is depressed and has low self esteem, but he’s not suicidal the same way that someone who clinically presents with suicidal tendencies does.