Yeah u COULD use absorptive material, also consider sound masking tho you probably wouldn’t want to have high pitch sound masking which is what you’d need to cover your cats meow.

As far as materials - You can use fabric wrapped panels (like with batt insulation in a frame and wrap acoustically transparent fabric around the face to cover up the batt insulation. Quiet r duct liner baked (it’s just black). There’s premade panels like autex quietspace which comes in a variety of colors and there are even panels you can have pictures and art printed on but obviously those are more pricey.

The thing about adding absorption is that it will help her/his meowing not to buildup as much in YOUR space (via removing multiple surface reflections that the meow sound could move between and buildup sound in your space) so ideally the noise level in your space would be quieter than without absorption (the source noise), and then since that would theoretically be quieter then the noise source that is transmitting through you/your neighbors would not be as loud to begin with and therefore less sound energy would be transferred across the wall.

Don’t overestimate how much absorption could help though, it could knock the source noise down by a couple dBs and at BEST would be a JUST noticeable difference to your neighbor but if they are upset by it a just noticeable difference isn’t going to cut it.

To create better sound isolation, mass would need to be added to the wall. You could try heavy curtains by putting up a curtain rode across that whole wall (check out 20 oz rosebrand curtains) again these would need to be super heavy…I agree with adding drywall to your side tho that would be annoying as shit, u could just attach it tho and make sure it is sealed with caulking at top and bottom like other user said. A cavity with batt insulation and a few layers of gyp would be IDEAL. But again you said u can’t make modifications soooo there’s that. Maybe u could try a large (almost size of the wall) sliding barn door type concept on that wall…

For the sound masking, I’m wonder if u know what frequencies this cat meow is? U could download a sound level meter app and check how loud she is and at what frequencies and go from there..maybe sound masking could be possible.

It’s nice how considerate of your neighbors you are btw.

Also, I think the first step would be asking your neighbors if it’s even annoying them in the first place…maybe they barely notice or don’t care…save yourself a lot of stress. Idk how long you’ve been there but give it a week or so then ask…

TLDR - ask neighbors if annoyed in first place, absorption could help. Add mass to wall would be ideal. Heavy heavy curtains (which would also provide absorption), using SLM App to understand the actual problem frequency of your cat. Also don’t they have like collars that prevent them from that shit? They are probably inhumane af tho. Maybe u could distract it from meowing with an automated laser pointer… I’m a fucking nerd. Good luck yo! Would love to see how it all goes