refactor!: Replace `httpx` with `impit` #601

Job	Run time
Docs check / Docs check	1m 4s
Unit tests / Unit tests (windows-latest, 3.10)	1m 23s
Unit tests / Unit tests (ubuntu-latest, 3.13)	29s
Type check / Type check (3.10)	27s
Unit tests / Unit tests (windows-latest, 3.12)	56s
Unit tests / Unit tests (ubuntu-latest, 3.11)	27s
Type check / Type check (3.12)	27s
Lint check / Lint check (3.10)	14s
Unit tests / Unit tests (windows-latest, 3.13)	59s
Unit tests / Unit tests (ubuntu-latest, 3.10)	27s
Type check / Type check (3.11)	27s
Unit tests / Unit tests (windows-latest, 3.11)	50s
Unit tests / Unit tests (ubuntu-latest, 3.12)	25s
Type check / Type check (3.13)	30s
Lint check / Lint check (3.12)	11s
Integration tests / Approve integration tests for PRs from forks	2m 35s
Integration tests / Integration tests	2m 35s
Lint check / Lint check (3.13)	13s
Lint check / Lint check (3.11)	16s
	14m 55s

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