ci: use `with-connect` action for Posit Connect integration tests (#351) #900

Job	Run time
Build Docs	1m 23s
Test Posit Connect	5m 51s
Tests (3.11, ubuntu-latest, --workers 4 --tests-per-worker 1)	3m 18s
Tests (3.13, ubuntu-latest, --workers 4 --tests-per-worker 1)	2m 8s
Tests (3.9, ubuntu-latest, --workers 4 --tests-per-worker 1)	3m 7s
Tests (windows-latest, 3.10, -k pins/tests)	15m 59s
Tests (3.12, ubuntu-latest, --workers 4 --tests-per-worker 1)	3m 6s
Tests (3.10, ubuntu-latest, --workers 4 --tests-per-worker 1)	2m 30s
Tests (ubuntu-latest, 3.9, requirements/minimum.txt)	5m 47s
Tests (macos-latest, 3.10, --workers 4 --tests-per-worker 1 -k pins/tests)	3m 50s
Test a fork PR (no secrets)	0s
Preview Docs:	-1s
Publish Docs	4s
Release to pypi	-1s
	47m 1s

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