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ci: Update vetiver tests to use with-connect #3021

Job	Run time
Vetiver integration test	3m 4s
prerelease-test	1m 42s
Integration tests against dev Connect	2m 42s
Integration tests against Connect 2023.03.0	2m 5s
test (py3.11 ubuntu-latest)	1m 26s
test (py3.9 ubuntu-latest)	1m 33s
test (py3.13 ubuntu-latest)	1m 34s
Integration tests against Connect 2025.09.0	2m 52s
test (py3.10 ubuntu-latest)	1m 41s
test (py3.13 windows-latest)	3m 48s
Integration tests against Connect release	3m 3s
Integration tests against Connect 2025.03.0	3m 16s
Integration tests against Connect 2022.10.0	2m 10s
test (py3.8 ubuntu-latest)	1m 41s
test (py3.13 macos-latest)	1m 36s
test (py3.12 ubuntu-latest)	1m 30s
Integration tests against Connect 2024.09.0	2m 21s
Integration tests against Connect 2024.03.0	2m 29s
Integration tests against Connect preview	2m 59s
Integration tests against Connect 2023.09.0	2m 13s
docs	23s
distributions (rsconnect)	53s
distributions (rsconnect_python)	49s
	47m 50s

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