Older cat behaviour advice

Hi, i dont have a lot of experience dealing with cats. im(m25) a first time cat dad and my kitty is young (1.5 years). however, my flatmates(m28) male cat is around 10 yrs old. since weve lived together for almost 2 years ive got really attached to this cat, even moreso now as ive been taking care of him quite a lot for the past 6 months as my flatmate got a bf and isnt around a lot. but as mentioned i dont really know much about older cats and i dont know whats normal and what could be concerning.

his cat rarely ever plays, doesnt have much movement and spends the majority of the time on his cat tree. well i am aware that cats just chill a lot but im worried this little movement could be bad for him health wise for joints etc. he gained a bit more weight but slowly hes been getting back in shape since we portion the food differently than before.

i dont want to ascribe human emotions to him but i also feel like a lot of his cat tree lying down could be due to him being upset hes left alone so much by my flatmate. could him being "depressed" make him less inclined to movement? i wish hed spend more time in my room with my cat but he seems very uprooted in my flatmates room which is understandable but him being alone so much breaks my heart. he also might have a cat asthma and has a lot of dandruff.

i cant do much since its not my cat but i care about him a lot. cant help but feel like hes slightly neglected and his unconditional love taken for granted