Thanks for the photo.
First - if you consider a rim too worn to use, don't use it. simple.
However - all three of mine look smoother than that!
The picture of the Ryde Andra on the SJS website shows it has a wear indicator, or rather it's a worn out indicator. It's the sort where one section of the extrusion is deliberately thinner than the rest, when it's worn you see a line appear, easier to see it than explain
https://www.sjscycles.co.uk/rims-tape/rigida-andra-30-26-559-mtb-css-rim-regular-drilling-black-32-hole/I've worn out a Sputnik that had the same thing, the rim is still solid when the indicator is visible. I'm assuming they've always been like that. but it's maybe something you can find out. If you google for images for "Rigida rim wear" you'll get some good photos of what to look out for.
I'm not convinced a squealing brake is a good sign of a worn rim, mine frequently do, even when new. I use Swisstop Salmon or BB Tristop pads, neither are cheap, but they last reasonably well, they may reduce squealing, I buy them for the superior braking. The front with a V brake sometimes squeals, it need a fair bit of toe in and sometimes adjusting mid wear. The front and rear with canti brakes never squeal, though there's lots of factors other than the brakes.
Then - clean you rim! I mean properly, give it a scrub with something fairly abrasive, your rim is likely to get a coating of brake block which certainly won't help.
