Well, in most .NET shops around me:
> The development and deployment tooling is so closely tied to VS that you can't really not use it.
Development tooling: It's 50-50. Some use Visual Studio, some use Rider. It's fine. The only drawback is that VS Live Share and the Jetbrains equivalent don't interoperate.
deployment tooling: There is deployment tooling tied to the IDE? No-one uses that, it seems like a poor idea. I see automated build/test/deploy pipelines in GitHib Actions, and in Octopus Deploy. TeamCity still gets used, I guess.
It's true though that the most common development OS is Windows by far (with Mac as second) and the most common deployment target by far is Linux.
However the fact that there is close to no friction in this dev vs deploy changeover means that the cross-platform stuff just works. At least for server-side things such as HTTP request and queue message processing. I know that the GUI toolkit story is more complex and difficult, but I don't have to deal with it at all so I don't have details or recommendations.
> is there deployment tooling tied to the IDE?
VS has the “Publish” functionality for direct deployment to targets. It works well for doing that and nothing else. As you said, CI/CD keeps deployment IDE agnostic and has far more capabilities (e.g. Azure DevOps, GitHub Actions).