If you are trying to recover files from an unreadable drive, than I'm not sure adding a Linux machine to the mix is going to help much.
If you install a fresh Win11 on a new SSD, then go ahead and do that.
Not sure what you mean when you say it 'doesn't work in the laptop but works in the caddy'.
You might need to explain exactly what you mean by that.
If it works in the caddy, then just plug the caddy into the freshly-installed machine as a secondary drive, and copy the files over?