Fix issues with nested widgets #17511

Job	Run time
Build VSIX	1m 14s
cancel_previous_runs	2s
Lint	1m 13s
Type Script Tests (ubuntu-latest, ts-unit)	1m 26s
Type Script Tests (windows-latest, ts-unit)	5m 27s
Tests (raw, python, 3.10, ^[^@]+$\|@mandatory\|@kernelCore\|@python\|@jupyter, ubuntu-latest)	5m 52s
Tests (raw, python, 3.10, @widgets, ubuntu-latest)	4m 39s
Tests (raw, python, 3.10, @iw, ubuntu-latest)	4m 3s
Tests (raw, python, 3.10, @webview\|@export\|@lsp\|@variableViewer, ubuntu-latest)	4m 12s
Tests (raw, python, 3.10, @debugger, ubuntu-latest)	3m 20s
Tests (remote, python, 3.10, ^[^@]+$\|@mandatory, ubuntu-latest)	3m 45s
Tests (web, python, 3.10, ^[^@]+$\|@mandatory, ubuntu-latest)	2m 54s
Tests (raw, python, 3.10, ^[^@]+$\|@mandatory, windows-latest)	4m 29s
Tests (raw, python, 3.10, @widgets, ubuntu-latest, 8)	4m 28s
Tests (remote, python, 3.10, @widgets, ubuntu-latest, 8)	5m 27s
Tests (raw, conda, 3.10, ^[^@]+$\|@mandatory\|@python, ubuntu-latest)	3m 21s
Tests (raw, noPython, @nonPython, ubuntu-latest)	2m 4s
Tests (remote, python, 3.10, @kernelCore, ubuntu-latest)	4m 20s
Smoke tests (ubuntu-latest, 3.10)	1m 31s
Smoke tests (windows-latest, 3.10)	2m 54s
Smoke tests (macos-latest, 3.10)	1m 36s
	1h 8m 17s

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