[release-17.0] Do not drain tablet in incremental backup (#13773)

[vitess-bot]

Description

This is a backport of #13773

[vitess-bot]

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[vitess-bot]

Hello @shlomi-noach, 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 13789 -R vitessio/vitess
git reset --hard origin/release-17.0
git cherry-pick -m 1 16024c2b7c2ceac9009d8174cad198159b64580b

[mattlord]

Why is this different in the v17 backport (new 2 file)? Aside from that, everything looks good. I just don't know why we now have builtinbackupengine2_test.go and builtinbackupengine_test.go in the backport.

[shlomi-noach]

Why is this different in the v17 backport (new 2 file)?

It's because of this: #13668 (comment) ; we refactored the test file names in main, but never backported it to release-17.0. The file go/vt/mysqlctl/builtinbackupengine_test.go is not your conventional unit test file and should not have been named the way it was: it uses a different package name than mysqlctl, which is the package that matches the directory where the file is located.

So, anyway, to add this new unit test, I had to create a new file in release-17.0.