fix(ci): Enable Docker builds and E2E for external PRs

[khvn26]

Thanks for submitting a PR! Please check the boxes below:

• [x] I have run pre-commit to check linting
• [x] I have added information to docs/ if required so people know about the feature!
• [x] I have filled in the "Changes" section below?
• [x] I have filled in the "How did you test this code" section below?
• [x] I have used a Conventional Commit title for this Pull Request

Changes

This does a few things:

• For PRs opened by external contributors, skip pushing built images to Github Container registry. Push to an ephemeral registry instead.
• For PRs opened by external contributors, skip building the Private cloud image altogether.
• Remove Private cloud E2E for PRs for now. When we have Private cloud-specific E2E scenarios, we'll be able to run them by adding a E2E job depending on private-cloud build.
• When running E2E, pull ephemeral Depot images if a Depot build ID was provided.
• When running E2E, display API container logs on failure as part of the Makefile target.
• Add secrets: inherit for the release/merge to main E2E run so errors are reported to Slack correctly.

How did you test this code?

Tested the Makefile change locally. The rest of the changes will be tested in CI.

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[matthewelwell]

Remove Private cloud E2E for PRs for now. When we have Private cloud-specific E2E scenarios, we'll be able to run them by adding a E2E job depending on private-cloud build.

So I guess we'll still run them against the private-cloud image on a merge to main?

[khvn26]

So I guess we'll still run them against the private-cloud image on a merge to main?

Yes we will.

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 96.57%. Comparing base (47eb149) to head (182cef2). Report is 3 commits behind head on main.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #4224 +/- ## ======================================= Coverage 96.57% 96.57% ======================================= Files 1190 1190 Lines 38754 38754 ======================================= Hits 37426 37426 Misses 1328 1328 ```

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