refactor!: Remove `Request.id` field #604

Job	Run time
Lint check / Lint check (3.11)	13s
Type check / Type check (3.13)	27s
Type check / Type check (3.10)	25s
Type check / Type check (3.11)	22s
Lint check / Lint check (3.12)	9s
Lint check / Lint check (3.13)	15s
Docs check / Docs check	51s
Lint check / Lint check (3.10)	13s
Type check / Type check (3.12)	25s
Unit tests / Unit tests (ubuntu-latest, 3.11)	25s
Unit tests / Unit tests (ubuntu-latest, 3.10)	26s
Unit tests / Unit tests (ubuntu-latest, 3.13)	25s
Unit tests / Unit tests (windows-latest, 3.13)	44s
Unit tests / Unit tests (ubuntu-latest, 3.12)	26s
Unit tests / Unit tests (windows-latest, 3.12)	50s
Unit tests / Unit tests (windows-latest, 3.10)	42s
Unit tests / Unit tests (windows-latest, 3.11)	42s
Integration tests / Integration tests (3.10)	17m 8s
Integration tests / Integration tests (3.13)	22m 54s
Integration tests / Approve integration tests for PRs from forks	5m 43s
Integration tests / Integration tests for PRs from forks	-1s
	53m 44s

Provide feedback