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ci: Update vetiver tests to use with-connect #2884

Job	Run time
prerelease-test	1m 33s
test (py3.8 ubuntu-latest)	1m 37s
test (py3.9 ubuntu-latest)	1m 25s
Integration tests against dev Connect	2m 47s
test (py3.12 ubuntu-latest)	1m 27s
test (py3.13 windows-latest)	3m 0s
test (py3.11 ubuntu-latest)	1m 30s
test (py3.13 macos-latest)	1m 31s
test (py3.10 ubuntu-latest)	1m 31s
Integration tests against Connect 2025.09.0	2m 57s
Integration tests against Connect release	3m 8s
Integration tests against Connect 2025.03.0	3m 36s
Integration tests against Connect 2022.10.0	2m 18s
Integration tests against Connect 2024.03.0	2m 25s
test (py3.13 ubuntu-latest)	1m 29s
Integration tests against Connect 2023.09.0	2m 28s
Integration tests against Connect 2023.03.0	2m 19s
Integration tests against Connect 2024.09.0	2m 29s
distributions (rsconnect)	43s
distributions (rsconnect_python)	46s
docs	26s
	41m 25s

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