fix: Save `RequestQueueState` for `FileSystemRequestQueueClient` in default KVS #3508

Job	Run time
Type check / Type check (3.12)	43s
Type check / Type check (3.11)	39s
Lint check / Lint check (3.10)	28s
Type check / Type check (3.13)	41s
Lint check / Lint check (3.11)	28s
Lint check / Lint check (3.12)	26s
Type check / Type check (3.10)	38s
Docs check / Docs check	1m 36s
Unit tests / Unit tests (ubuntu-latest, 3.13)	2m 12s
Lint check / Lint check (3.13)	29s
Unit tests / Unit tests (windows-latest, 3.11)	3m 22s
Unit tests / Unit tests (windows-latest, 3.12)	3m 7s
Unit tests / Unit tests (ubuntu-latest, 3.12)	2m 5s
Unit tests / Unit tests (windows-latest, 3.13)	3m 58s
Unit tests / Unit tests (windows-latest, 3.10)	3m 27s
Unit tests / Unit tests (ubuntu-latest, 3.10)	2m 9s
Unit tests / Unit tests (ubuntu-latest, 3.11)	2m 14s
	28m 42s

Provide feedback