fix(webkit): stabilize inspector connections and panel state #294

Job	Run time
Rust lint and unit tests	1m 39s
Build integration artifacts	3m 6s
Packages and VS Code extension	31s
Client lint, build, and tests	28s
Android emulator integration	5m 50s
CLI simulator integration	11m 48s
JS API simulator integration	4m 22s
	27m 44s

Provide feedback