Sometimes mental health and depression can get so bad that doing something like taking a shower really can seem impossible. Or if you're struggling with addiction, it can be a big turning point when you start brushing your teeth and going to bed instead of just passing out while drinking. etc. In situations like that, yeah, it's absolutely something you should feel proud of doing and it's fine to share that like an accomplishment.
I doubt he has any mental health issues beyond just situational stuff. He's functioning well enough to maintain a job and go to things like karaoke regularly. so it's really bizarre to read him talking about showering like he had to overcome something to do it.
Chibi, if you're reading this: good job showering. Now do it every day like all the rest of us who feel kind of crappy sometimes.