fix: use internal custom_headers #1399

Job	Run time
Check permission	1s
Schedule run ci / Attach dartdoc	1m 26s
Schedule run ci / Flutter unit test	54s
Schedule run ci / Flutter codestyle/analyze check	3m 4s
Schedule run ci / Run Flutter Android Integration Tests (3.7.0)	17m 3s
Schedule run ci / pub publish check	47s
Schedule run ci / Run Flutter iOS Integration Tests (3.7.0)	17m 20s
Schedule run ci / Run Flutter macOS Integration Tests (3.7.0)	17m 19s
Schedule run ci / Run Flutter iOS Integration Tests (3.16)	18m 50s
Schedule run ci / Run Flutter Web Integration Tests (3.x)	3m 21s
Schedule run ci / Run Flutter Windows Integration Tests (3.7.0)	14m 24s
Schedule run ci / Build Android on Ubuntu (3.7.12)	5m 11s
Schedule run ci / Build iOS (3.7.0)	2m 44s
Schedule run ci / Build Android on Windows (3.7.12)	12m 0s
Schedule run ci / Build iOS with xcode 15.x (3.x)	4m 19s
Schedule run ci / Build Web (3.7.0)	1m 2s
Schedule run ci / Run Flutter Android Rendering Tests	19m 55s
Schedule run ci / Check android15 16k page size alignment (3.x)	5m 15s
Schedule run ci / Run Flutter iOS Rendering Tests (3.x)	14m 1s
Schedule run ci / Run Flutter macOS Rendering Tests (3.x)	16m 42s
Schedule run ci / Run Flutter Web Rendering Tests (3.x)	3m 29s
Schedule run ci / Run Flutter Windows Rendering Tests (3.x)	20m 1s
	3h 19m 8s

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