chore: moved user agent to logging category api #789

Job	Run time
test / test-flutter-vm (stable, any)	4m 25s
test / test-flutter-vm (stable, any)	4m 25s
test / test-flutter-vm (stable, 3.10.1)	4m 33s
test / test-flutter-vm (stable, 3.10.1)	4m 33s
e2e_android_test / e2e-test-android (24)	39m 6s
e2e_android_test / e2e-test-android (24)	39m 6s
e2e_linux_test / e2e-test-linux	26m 19s
e2e_linux_test / e2e-test-linux	26m 19s
e2e_android_test / e2e-test-android (33)	38m 34s
e2e_android_test / e2e-test-android (33)	38m 34s
e2e_ios_test / e2e-test-ios	33m 10s
e2e_ios_test / e2e-test-ios	37m 9s
e2e_web_test / e2e-test-web	37m 8s
e2e_web_test / e2e-test-web	34m 13s
e2e_windows_test / e2e-test-windows	39m 28s
e2e_windows_test / e2e-test-windows	39m 28s
	7h 26m 30s

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