fix: Fix flaky test_common_headers_and_user_agent #2324

Job	Run time
Docs check / Docs check	1m 14s
Type check / Type check (3.9)	42s
Lint check / Lint check (3.9)	29s
Type check / Type check (3.10)	44s
Unit tests / Unit tests (ubuntu-latest, 3.9)	2m 34s
Type check / Type check (3.11)	39s
Lint check / Lint check (3.10)	22s
Type check / Type check (3.12)	44s
Lint check / Lint check (3.11)	25s
Type check / Type check (3.13)	41s
Lint check / Lint check (3.12)	27s
Unit tests / Unit tests (ubuntu-latest, 3.10)	2m 45s
Lint check / Lint check (3.13)	29s
Unit tests / Unit tests (ubuntu-latest, 3.11)	2m 50s
Unit tests / Unit tests (ubuntu-latest, 3.12)	2m 57s
Unit tests / Unit tests (ubuntu-latest, 3.13)	2m 27s
Unit tests / Unit tests (windows-latest, 3.9)	4m 2s
Unit tests / Unit tests (windows-latest, 3.10)	3m 42s
Unit tests / Unit tests (windows-latest, 3.11)	4m 23s
Unit tests / Unit tests (windows-latest, 3.12)	4m 31s
Unit tests / Unit tests (windows-latest, 3.13)	4m 6s
	41m 13s

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