I have a similar drain as yours and I’ve been using this:
LEKEYE Shower Drain Hair Catcher/Strainer/Stainless Steel and Silicone https://www.amazon.com/dp/B06W2MPGZV/ref=cm_sw_r_cp_api_fabt1_rj2TFbB4CYPZG?_encoding=UTF8&psc=1
It works pretty well!
That would work, but the one I'm thinking of is something more like this
The Dollar Store one is more cheaply made - no silicone ring around the edge, which is a good thing because it lays flat against the tub instead of being raised that little bit, which allows hairs to get under.
Also the Dollar Store one has little feet that go into the drain to hold it in place.
There's probably a trap around the lip of the drain, hard to tell from the photo. The design is rather annoying though and gets clogged with hair and whatnot pretty quickly, which is nasty to remove because it's just sitting in water. I got a hair catcher to replace the cover like this one: https://www.amazon.co.uk/gp/product/B06W2MPGZV/
Someone already said to brush his hair before shower. What I (longhaired) also do is stroke my hair while washing it and applying conditioner and grabbing onto whatever loose hair comes off, and then I stick it to the shower wall so it doesn't get washed down the drain. When I'm done with my shower I grab the hair mess off the wall and throw it in the bin.
Something like this might also help: https://www.amazon.com/LEKEYE-Catcher-Strainer-Stainless-Silicone/dp/B06W2MPGZV
But its your hair? That still affects you?
Unless your dropping draino down your pipes every few days you really gotta stop it from going down. This atleast you can pick it up and not directly touch it since its larger. Just tap the side againt the trash and it should come off. Also what if you used like tweezers or longer thin tongs to pick up the hair so technically it's not your bare hands and wear gloves? No touch = less drama in my mind
https://www.amazon.com/LEKEYE-Catcher-Strainer-Stainless-Silicone/dp/B06W2MPGZV
https://www.amazon.com/LEKEYE-Catcher-Strainer-Stainless-Silicone/dp/B06W2MPGZV
Here's a link to one on Amazon