The advantage of TomEE is that it comes with all kinds of libraries built in, JAX-RS amongst them. I've never seen a particular need for that, and just use plain Tomcat. Build system like Maven and Gradle make it easy to pull in external dependencies like JAX-RS, and Tomcat is much more widely used than TomEE, so in case of issues it's easier to find answers online.
I've also never seen a need for frameworks like RestEasy or CXF - I just use Jersey, the JAX-RS reference implementation. But maybe those other frameworks add some fantastic APIs on top of that; I don't know.
As Tim H said, migrating from javax to jakarta (and from Tomcat 9 to Tomcat 10) may require some adjustments in terms of which libraries to pull in, but you need to do that anyway at some point. In my experience, it was pretty much painless.
I haven't migrated to JAX-RS 3 yet, but I doubt that it involves much more than changing import statements and maybe some configuration settings.