Fix issues with nested widgets #17510

Job	Run time
Lint	1m 3s
cancel_previous_runs	2s
Build VSIX	1m 16s
Type Script Tests (ubuntu-latest, ts-unit)	56s
Tests (raw, python, 3.10, ^[^@]+$\|@mandatory\|@kernelCore\|@python\|@jupyter, ubuntu-latest)	1m 26s
Type Script Tests (windows-latest, ts-unit)	2m 46s
Tests (raw, python, 3.10, @widgets, ubuntu-latest)	1m 47s
Tests (raw, python, 3.10, @iw, ubuntu-latest)	1m 37s
Tests (raw, python, 3.10, @webview\|@export\|@lsp\|@variableViewer, ubuntu-latest)	1m 32s
Tests (raw, python, 3.10, @debugger, ubuntu-latest)	1m 46s
Tests (remote, python, 3.10, ^[^@]+$\|@mandatory, ubuntu-latest)	1m 43s
Tests (web, python, 3.10, ^[^@]+$\|@mandatory, ubuntu-latest)	1m 45s
Tests (raw, python, 3.10, ^[^@]+$\|@mandatory, windows-latest)	3m 11s
Tests (raw, python, 3.10, @widgets, ubuntu-latest, 8)	1m 34s
Tests (remote, python, 3.10, @widgets, ubuntu-latest, 8)	1m 43s
Tests (raw, conda, 3.10, ^[^@]+$\|@mandatory\|@python, ubuntu-latest)	2m 4s
Tests (raw, noPython, @nonPython, ubuntu-latest)	1m 8s
Tests (remote, python, 3.10, @kernelCore, ubuntu-latest)	2m 3s
Smoke tests (ubuntu-latest, 3.10)	1m 0s
Smoke tests (windows-latest, 3.10)	3m 18s
Smoke tests (macos-latest, 3.10)	1m 11s
	34m 51s

Provide feedback