chore(suite): separate popup logic from `@suite-common/connect-init` #9322

Job	Run time
Setup and Cache Dependencies	1m 49s
Linting and formatting	2m 19s
Unit Tests	3m 56s
Other Checks	1m 49s
Build libs for publishing	1m 45s
Releases revision Checks	1m 51s
Type Checking	5m 37s
	19m 6s

Provide feedback