race in docs build causes build failure unrelated to changes

Start with the docs build process and the Buildkite log around the git push origin beats_bk_39588 step. Reproduce or trace concurrent builds targeting the same branch, then verify that unrelated documentation builds no longer fail because a remote branch was updated by another process.

Not infrequently I see docs build failure due to what looks to be a race condition in the build architecture. This is demonstrated by this buildkite log tail

<snip>
INFO:build_docs:  Branch: 8.9, Version: 8.9
INFO:build_docs:  Branch: main, Version: master
INFO:build_docs:All cross-document links OK
INFO:build_docs:Saving branch tracker
INFO:build_docs:Building sitemap
INFO:build_docs:Commiting changes
INFO:build_docs:Pushing changes
INFO:build_docs:Error executing: git push origin beats_bk_39588 in GIT_DIR /docs_build/.repos/target_repo.git
INFO:build_docs:---out---
INFO:build_docs:
INFO:build_docs:---err---
INFO:build_docs:Failed to add the ECDSA host key for IP address '140.82.112.3' to the list of known hosts (/tmp/.ssh/known_hosts).
INFO:build_docs:To github.com:elastic/built-docs
INFO:build_docs: ! [rejected]                    beats_bk_39588 -> beats_bk_39588 (fetch first)
INFO:build_docs:error: failed to push some refs to 'git@github.com:elastic/built-docs'
INFO:build_docs:hint: Updates were rejected because the remote contains work that you do
INFO:build_docs:hint: not have locally. This is usually caused by another repository pushing
INFO:build_docs:hint: to the same ref. You may want to first integrate the remote changes
INFO:build_docs:hint: (e.g., 'git pull ...') before pushing again.
INFO:build_docs:hint: See the 'Note about fast-forwards' in 'git push --help' for details.
INFO:build_docs:
INFO:build_docs:---------
:rotating_light: Error: The command exited with status 1
user command error: exit status 1

AFAIUI this is due to the build architecture assuming that it is a sequential process, when it is not, and so assuming that it can push to a branch that is not owned solely by the pushing process.