refactor!: Remove `Request.id` field #602

Job	Run time
Type check / Type check (3.11)	26s
Type check / Type check (3.12)	24s
Type check / Type check (3.10)	25s
Lint check / Lint check (3.13)	17s
Type check / Type check (3.13)	29s
Lint check / Lint check (3.12)	10s
Lint check / Lint check (3.10)	11s
Unit tests / Unit tests (windows-latest, 3.11)	54s
Unit tests / Unit tests (ubuntu-latest, 3.12)	25s
Unit tests / Unit tests (ubuntu-latest, 3.10)	30s
Docs check / Docs check	57s
Unit tests / Unit tests (ubuntu-latest, 3.13)	27s
Lint check / Lint check (3.11)	15s
Unit tests / Unit tests (windows-latest, 3.13)	1m 8s
Unit tests / Unit tests (windows-latest, 3.12)	59s
Unit tests / Unit tests (windows-latest, 3.10)	50s
Integration tests / Integration tests (3.13)	16m 47s
Unit tests / Unit tests (ubuntu-latest, 3.11)	23s
Integration tests / Integration tests (3.10)	16m 39s
Integration tests / Approve integration tests for PRs from forks	0s
Integration tests / Integration tests for PRs from forks	0s
	42m 36s

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