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I don't think so.
Currently, the only scope for a shared service is one build and continuous mode is not one build, but just keeping the frontend running, retriggering the build if inputs changed.

But you might add your use-case to <https://github.com/gradle/gradle/issues/27756> maybe it is also possible to have this broader scope added.

I was also pretty sure it wasn't possible today.
Thanks for the issue link.