@Jockette
It's not so much yoga as gentle stretching. You said you're careful with movements so I guess that means when you stretch?
If you can get into a gentle stretching routine that's all you need until you feel stronger and more confident to try something else.
The key is to do it regularly.
In my case, I was going to pt last year for my back and hip. It helped so much that I do those home exercises and add some yoga poses. It's what makes YOU feel better. You don't have to follow any organized program.
I make it a point to at least do the pt exercises each day. If I feel like adding yoga then I do. I spend a lot of time on the floor.
Does yoga help athritis? I don't know. I know it helps with my flexibility, posture, and feeling of well being. I have arthritis almost everywhere. After my tkr, hubs illness, the holidays I wanted to curl up in a ball LOL! It hurt to move. Then I forced myself to start moving and stretching. Little by little I've come to a good place. And the regulated "yoga breathing" feels like fresh air when you've finished .
Talk to the instructor at the clubhouse yoga. Maybe you can sit in on classes to see what it's all about. I bet the students would be very welcoming. They were all beginners in the beginning!
This morning I walked with Tootsie for a very long time. Then made breakfast, straightened the apartment, a little laundry, then bathed and groomed Toots. I'm laying in the bed with an ice pack on my back. It is what it is.

ODIC but not knee related.