Remove usage of project.privacy_level

[stsewd]

Test should pass after #6535

If this is approved I can create a redirect to the new section.

Closes #4743
Partially closes / #2663

[humitos]

Makes sense to me. We can merge it after today's deploy.

[ericholscher]

This seems simple enough, it's mostly just finishing up the work we've been doing previously. Is there any change required on .com here? Are we removing it there too?

[stsewd]

@ericholscher yes, it's #878 on corp.

Fix for the flaky tests in on #7137

[ericholscher]

@stsewd need the redirect now 👍