Make more token types work as $HOMEBREW_GITHUB_API_TOKEN #26617

Job	Run time
syntax	48s
vendored gems	47s
tap syntax	4m 47s
formula audit	6m 28s
docker	4m 49s
cask audit	2m 48s
test default formula (Ubuntu 22.04)	4m 14s
test default formula (Ubuntu 20.04)	5m 30s
test default formula (macOS 13 x86_64)	2m 30s
tests (online)	7m 40s
update-test (Ubuntu 22.04)	1m 2s
test default formula (macOS 14 arm64)	1m 26s
tests (generic OS)	6m 34s
update-test (macOS 13)	1m 3s
tests (Ubuntu 22.04)	5m 38s
tests (Ubuntu 20.04)	6m 13s
tests (macOS 13 x86_64)	6m 56s
tests (macOS 14 arm64)	6m 25s
	1h 15m 38s

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