[release-21.0] BuiltinBackupEngine: Retry file close and fail backup when we cannot (#18848)

[vitess-bot]

Description

This is a backport of #18848

[vitess-bot]

Hello @mattlord, there are conflicts in this backport.

Please address them in order to merge this Pull Request. You can execute the snippet below to reset your branch and resolve the conflict manually.

Make sure you replace origin by the name of the vitessio/vitess remote

git fetch --all
gh pr checkout 18860 -R vitessio/vitess
git reset --hard origin/release-21.0
git cherry-pick -m 1 1fe6c6809479fa9e0ab740a788f0e19d1ec60914

[vitess-bot]

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[mattlord]

The builtin backup engine is significantly different in v21, so I'm going to close this as it's EOL soon and I don't want to risk destabilizing it for something that should be exceedingly rare.

I also checked to see if it had the general error handling issue fixed in the parent PR, but it does not have those issues. Those were introduced in later work.