Ensure kernel points to live kernel connection when starting remote kernels

[DonJayamanne]

Fixes #9865

[codecov-commenter]

Codecov Report

Merging #10573 (b37d24c) into main (1d727e8) will increase coverage by 0%. The diff coverage is 70%.

@@           Coverage Diff           @@
##            main   #10573    +/-   ##
=======================================
  Coverage     63%      63%            
=======================================
  Files        477      479     +2     
  Lines      34162    34378   +216     
  Branches    5546     5576    +30     
=======================================
+ Hits       21597    21812   +215     
+ Misses     10506    10503     -3     
- Partials    2059     2063     +4     

Impacted Files	Coverage Δ
src/kernels/types.ts	100% <ø> (ø)
src/notebooks/controllers/types.ts	100% <ø> (ø)
src/kernels/notebookControllerWrapper.ts	34% <34%> (ø)
src/kernels/common/delayedFutureExecute.ts	5% <50%> (+1%)	:arrow_up:
src/kernels/kernelProvider.base.ts	93% <68%> (-3%)	:arrow_down:
src/notebooks/controllers/kernelConnector.ts	82% <71%> (-1%)	:arrow_down:
...rc/notebooks/controllers/controllerRegistration.ts	85% <80%> (-2%)	:arrow_down:
src/kernels/kernelConnectionMetadataWrapper.ts	80% <80%> (ø)
src/interactive-window/interactiveWindow.ts	75% <85%> (+<1%)	:arrow_up:
...ebooks/controllers/notebookIPyWidgetCoordinator.ts	89% <88%> (+2%)	:arrow_up:
... and 41 more

[IanMatthewHuff]

Looks like there is a new failed test: 3rd Party Kernel Service API Start Kernel

[rchiodo]

I wonder if we could tag all of this code with 'Unnecessary if we could get a new API for creating controllers'? Maybe a comment in some key places?