BridgeJS: Remove BridgeType usage from ts2swift #1953

Job	Run time
Build for native target (macos-15, Xcode_16.4)	2m 33s
format	33s
build-examples	42m 59s
check-bridgejs-generated	2m 40s
Build and Test (ubuntu-24.04, https://download.swift.org/swift-6.3-branch/ubuntu2404/swift-6.3-DE...	12m 50s
Build and Test (ubuntu-22.04, https://download.swift.org/swift-6.1-release/ubuntu2204/swift-6.1-R...	13m 19s
Build and Test (ubuntu-22.04, https://download.swift.org/development/ubuntu2204/swift-DEVELOPMENT...	17m 42s
Build and Test (ubuntu-24.04, https://download.swift.org/development/ubuntu2404/swift-DEVELOPMENT...	13m 22s
deploy-examples	0s
	1h 45m 58s

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