fix(webview): sync cachedState on mode changes in SettingsView #3108

Job	Run time
compile	2m 15s
dependency-review	10s
platform-unit-test (ubuntu-latest)	4m 51s
check-translations	41s
knip	50s
platform-unit-test (windows-latest)	7m 52s
invisible-chars	7s
	16m 46s

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