Implementation for kernel reconnection + tests

[suprjinx]

Fixes #3998

[suprjinx]

@microsoft-github-policy-service agree company="G-Research OSS"

[DonJayamanne]

@suprjinx thank you for submitting this PR.
Wanted to leave a comment on this before you spend more time on this.
Unfortunately we will not be able to take this PR, as this relies on spinning up Jupyter server locally.
Not everyone will have Jupyter lab/notebook installed. let alone Python.
The Jupyter extension works with Kernels such as R, Julia and the like even without installing Python/Jupyter.

Enforcing such a limitation wouldn't work for all
Besides you can already spin up a Jupyter application externally and connect to that using Jupyter extension and the connections are never lose. I.e. even after you shutdown VS Code and restart it, it will re-connect to the same server/kernels.

Again, thank you for submitting this PR and attempting to fix this, however I cannot take this due to above mentioned issues.

[suprjinx]

@DonJayamanne thanks for the feedback -- what do you think of simpler implementation that just offers an option to start server in the kernel connection chooser eg:

The idea would be a Launch Persistent Server command that runs jupyter server, and we then connect using the Existing Server pathway. Implemented here: #16915

Re: users who don't have Jupyter installed -- perhaps we could disable this option when there are no python environments available.