Enable changing the file extension of files created when using the "Create Declaration / Definition"

Discussed in https://github.com/microsoft/vscode-cpptools/discussions/10969

^{Originally posted by starball5 May 18, 2023}
It seems (or maybe I'm wrong) that in c++ header files, using the "Create Declaration / Definition" context menu action on a declaration will always create definition files with ".cpp" as the file extension.

Is it possible to change that file extension to anything else? (Ex. ".cc" or ".cxx"?)

I tried looking through the source code and found the following code for the extension client that handles the server response, but it's not very enlightening into what the server side does.

https://github.com/microsoft/vscode-cpptools/blob/v1.15.4/Extension/src/LanguageServer/client.ts#L3519

I gave a few minutes of nm -nC, strings, objdump -SCd of my installed cpptools-srv binary, and then threw in the towel figuring I was out of my depth with those tools.

Also potentially loosely related: https://github.com/Microsoft/vscode-cpptools/issues/1341.

Start with Extension/src/LanguageServer/client.ts around line 3519 and read discussion #10969, then trace how the server handles the Create Declaration / Definition response. Done means users can choose an alternative definition-file extension such as .cc or .cxx instead of always receiving .cpp, with the behavior verified in the relevant extension workflow.