[NFC] Use angle-bracketed includes in public headers #2773

Job	Run time
catalyst	5m 31s
integration	6m 25s
pod-lib-lint (ios, macos-12)	9m 20s
quickstart	5m 0s
pod-lib-lint (ios, macos-13)	9m 0s
pod-lib-lint (tvos, macos-12)	9m 31s
pod-lib-lint (tvos, macos-13)	9m 19s
pod-lib-lint (macos --skip-tests, macos-12)	6m 0s
pod-lib-lint (macos --skip-tests, macos-13)	6m 1s
spm (iOS, macos-12)	7m 46s
spm (iOS, macos-13)	14m 48s
pod-lib-lint (watchos, macos-12)	5m 41s
spm (tvOS, macos-12)	9m 11s
pod-lib-lint (watchos, macos-13)	7m 5s
spm (tvOS, macos-13)	9m 47s
spm (macOS, macos-12)	4m 40s
spm (macOS, macos-13)	6m 44s
spm (catalyst, macos-12)	5m 3s
spm (catalyst, macos-13)	7m 32s
spm (watchOS, macos-12)	5m 59s
spm (watchOS, macos-13)	8m 11s
database-cron-only	0s
	2h 38m 34s

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