refactor!: Replace `httpx` HTTP client with `impit` #349

Job	Run time
Type check / Type check (3.11)	14s
Type check / Type check (3.12)	16s
Type check / Type check (3.9)	19s
Async dostrings check / Async docstrings check	17s
Type check / Type check (3.13)	18s
Lint check / Lint check (3.9)	10s
Lint check / Lint check (3.10)	12s
Lint check / Lint check (3.12)	8s
Lint check / Lint check (3.11)	14s
Type check / Type check (3.10)	19s
Unit tests / Unit tests (ubuntu-latest, 3.12)	25s
Unit tests / Unit tests (ubuntu-latest, 3.10)	24s
Unit tests / Unit tests (windows-latest, 3.9)	44s
Unit tests / Unit tests (ubuntu-latest, 3.9)	24s
Unit tests / Unit tests (ubuntu-latest, 3.11)	23s
Lint check / Lint check (3.13)	12s
Unit tests / Unit tests (windows-latest, 3.11)	41s
Unit tests / Unit tests (windows-latest, 3.12)	45s
Unit tests / Unit tests (windows-latest, 3.10)	40s
Unit tests / Unit tests (ubuntu-latest, 3.13)	23s
Unit tests / Unit tests (windows-latest, 3.13)	38s
Docs check / Docs check	1m 7s
Integration tests / Approve integration tests for PRs from forks	3s
Integration tests / Integration tests	0s
Integration tests / Integration tests for PRs from forks	0s
	9m 16s

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