Revert "Update nightly tag every night (#17879)" (#18133)

This PR reverts #17879, as it wasn't working.

When a GitHub Action pushes a tag, it does not trigger workflows for
push events for that tag:

> When you use the repository's `GITHUB_TOKEN` to perform tasks, events
triggered by the `GITHUB_TOKEN`, with the exception of
`workflow_dispatch` and `repository_dispatch`, will not create a new
workflow run. This prevents you from accidentally creating recursive
workflow runs. For example, if a workflow run pushes code using the
repository's `GITHUB_TOKEN`, a new workflow will not run even when the
repository contains a workflow configured to run when `push` events
occur.
>
> —
[source](https://docs.github.com/en/actions/security-for-github-actions/security-guides/automatic-token-authentication#using-the-github_token-in-a-workflow)

This reverts commit 761129e3739efacb7b8763eaa0fa8a109e935447.

Release Notes:

- N/A