Bump to TypeScript 5.5 and enable `noImplicitAny` #1433

Job	Run time
build-desktop (macos, development)	1m 48s
build-desktop (macos, production)	1m 46s
build-desktop (ubuntu, development)	53s
build-desktop (ubuntu, production)	52s
build-desktop (windows, development)	3m 29s
build-desktop (windows, production)	4m 4s
build-docker (macos-13)	22m 49s
build-docker (ubuntu-latest)	2m 24s
build-web (macos, development)	59s
build-web (macos, production)	1m 36s
build-web (macos, test)	1m 9s
build-web (ubuntu, development)	1m 4s
build-web (ubuntu, production)	1m 2s
build-web (ubuntu, test)	57s
build-web (windows, development)	4m 9s
build-web (windows, production)	3m 57s
build-web (windows, test)	4m 43s
	57m 41s

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