Restore manual `Client` cleanup on session logout #11034

Job	Run time
Search for invalid dependencies	1m 13s
Search for invalid screenshot files	5s
Search for forbidden patterns	7s
Check shell scripts	6s
Detekt checks	1m 44s
Knit checks	1m 6s
Konsist tests	3m 0s
Ktlint checks	2m 11s
Android lint check	13m 0s
Project Check Suite	1m 15s
	23m 47s

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