Fix issues with nested widgets #17514

Job	Run time
cancel_previous_runs	2s
Type Script Tests (ubuntu-latest, ts-unit)	1m 20s
Type Script Tests (windows-latest, ts-unit)	5m 1s
Build VSIX	1m 19s
Lint	1m 58s
Tests (raw, python, 3.10, ^[^@]+$\|@mandatory\|@kernelCore\|@python\|@jupyter, ubuntu-latest)	5m 55s
Tests (raw, python, 3.10, @widgets, ubuntu-latest)	4m 15s
Tests (raw, python, 3.10, @iw, ubuntu-latest)	3m 45s
Tests (raw, python, 3.10, @webview\|@export\|@lsp\|@variableViewer, ubuntu-latest)	4m 31s
Tests (raw, python, 3.10, @debugger, ubuntu-latest)	3m 16s
Tests (remote, python, 3.10, ^[^@]+$\|@mandatory, ubuntu-latest)	3m 58s
Tests (web, python, 3.10, ^[^@]+$\|@mandatory, ubuntu-latest)	2m 56s
Tests (raw, python, 3.10, ^[^@]+$\|@mandatory, windows-latest)	6m 50s
Tests (raw, python, 3.10, @widgets, ubuntu-latest, 8)	4m 33s
Tests (remote, python, 3.10, @widgets, ubuntu-latest, 8)	5m 32s
Tests (raw, conda, 3.10, ^[^@]+$\|@mandatory\|@python, ubuntu-latest)	3m 26s
Tests (raw, noPython, @nonPython, ubuntu-latest)	1m 44s
Tests (remote, python, 3.10, @kernelCore, ubuntu-latest)	3m 58s
Smoke tests (ubuntu-latest, 3.10)	1m 32s
Smoke tests (windows-latest, 3.10)	4m 47s
Smoke tests (macos-latest, 3.10)	1m 38s
	1h 12m 16s

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