Ok so the good news is that we know how to do this correctly, since watch expressions are evaluated as intended:

Debugging it reveals that hovering over "${module}" is processed by the hover handler (which just gets the symbol details and returns that it's a variable with the name module) and hovering over "$module" actually goes through the code lens handler.

To be continued...

I think what's going on is that, while debugging, VS Code automatically looks up the values of symbols on hover if they are variables. So $module is recognized as a variable because of its symbol type, but ${module} is not (it's an expression). I actually plumbed in logic to evaluate variables on hover and it works like you'd expect (though I haven't fixed up the formatting).

So like when I have all LSP messages getting logged, when not debugging I see a hover request go across for both ${module} and $module, but when debugging I only see a hover request go across for ${module}, there is no request being sent for $module which is what makes me think VS Code is doing a client-side lookup for the variable's value based on the already known list of variables and their values (since the debugger is stopped).