Buildkite pipeline for integration tests

[JoshMock]

Adds a Buildkite pipeline to run client integration tests. Will drop the Jenkins job definitions once I've verified this runs as expected.

[JoshMock]

Buildkite keeps failing these new jobs, telling me that the tsc executable is not found on PATH. When I run the same Docker image locally, it finds tsc with no problem. 🤷‍♂️ Will keep poking at it.

[JoshMock]

Finally got it: the docker run in run-repository.sh was mapping volumes that overwrote the results of npm install. Doing a COPY of everything into the image instead of mapping volumes works like a charm.

[github-actions]

The backport to 8.7 failed:

The process '/usr/bin/git' failed with exit code 1

To backport manually, run these commands in your terminal:

# Fetch latest updates from GitHub
git fetch
# Create a new working tree
git worktree add .worktrees/backport-8.7 8.7
# Navigate to the new working tree
cd .worktrees/backport-8.7
# Create a new branch
git switch --create backport-1863-to-8.7
# Cherry-pick the merged commit of this pull request and resolve the conflicts
git cherry-pick --mainline 1 c9f31d22fdba2d73f7829f07792acde330ae0e04
# Push it to GitHub
git push --set-upstream origin backport-1863-to-8.7
# Go back to the original working tree
cd ../..
# Delete the working tree
git worktree remove .worktrees/backport-8.7

Then, create a pull request where the base branch is 8.7 and the compare/head branch is backport-1863-to-8.7.