chore: Update public url handling #696

Job	Run time
Type check / Type check (3.13)	28s
Type check / Type check (3.12)	31s
Lint check / Lint check (3.12)	16s
Type check / Type check (3.11)	29s
Type check / Type check (3.10)	23s
Lint check / Lint check (3.10)	14s
Lint check / Lint check (3.13)	14s
Docs check / Docs check	1m 0s
Unit tests / Unit tests (windows-latest, 3.10)	53s
Unit tests / Unit tests (ubuntu-latest, 3.11)	27s
Lint check / Lint check (3.11)	11s
Unit tests / Unit tests (ubuntu-latest, 3.12)	28s
Unit tests / Unit tests (windows-latest, 3.11)	51s
Unit tests / Unit tests (ubuntu-latest, 3.13)	28s
Unit tests / Unit tests (ubuntu-latest, 3.10)	27s
Unit tests / Unit tests (windows-latest, 3.12)	43s
Unit tests / Unit tests (windows-latest, 3.13)	48s
Integration tests / Integration tests (3.10)	21m 1s
Integration tests / Integration tests (3.13)	21m 5s
Integration tests / Approve integration tests for PRs from forks	0s
Integration tests / Integration tests for PRs from forks	0s
	50m 57s

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