Your PS5 analog sticks are melting!
UPDATE: A few folks told me that WD-40 works to resolve this and… they were kind of right! Just buy a pen applicator and dab it on.
Years ago, I unpacked an old PS3 and was disgusted to realize that the controllers' analog sticks had all melted into gooey, sticky black blobs. I wondered if they'd gotten too hot at some point, somehow, but it turns out that the low-grade rubber and oil Sony used just inevitably denatures over time. I figured they'd have fixed this in later generations, but it turns out they haven't! Both my PS5 controllers are now completely unusable after sitting idle for six months.
Entropy always wins… neat!