feat: implement task resumption from web UI #13986

Job	Run time
knip	51s
check-translations	34s
compile	1m 55s
platform-unit-test (windows-latest)	6m 14s
check-openrouter-api-key	3s
platform-unit-test (ubuntu-latest)	3m 43s
integration-test	0s
notify-slack-on-failure	0s
	13m 20s

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