Add GitHub Actions workflow to trigger docs-staging nextgen update

[qiancai]

First-time contributors' checklist

• I've signed the Contributor License Agreement, which is required for the repository owners to accept my contribution.

What is changed, added or deleted? (Required)

Which TiDB version(s) do your changes apply to? (Required)

Tips for choosing the affected version(s):

By default, CHOOSE MASTER ONLY so your changes will be applied to the next TiDB major or minor releases. If your PR involves a product feature behavior change or a compatibility change, CHOOSE THE AFFECTED RELEASE BRANCH(ES) AND MASTER.

For details, see tips for choosing the affected versions (in Chinese).

• master (the latest development version)
• v9.0 (TiDB 9.0 versions)
• v8.5 (TiDB 8.5 versions)
• v8.1 (TiDB 8.1 versions)
• v7.5 (TiDB 7.5 versions)
• v7.1 (TiDB 7.1 versions)
• v6.5 (TiDB 6.5 versions)
• v6.1 (TiDB 6.1 versions)
• v5.4 (TiDB 5.4 versions)

What is the related PR or file link(s)?

• This PR is translated from: Add GitHub Actions workflow to trigger docs-staging nextgen update docs#22342
• Other reference link(s):

Do your changes match any of the following descriptions?

• Delete files
• Change aliases
• Need modification after applied to another branch
• Might cause conflicts after applied to another branch

[lilin90]

/lgtm

[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2026-01-19 03:32:41.323754126 +0000 UTC m=+378388.937710983: ☑️ agreed by lilin90.

[qiancai]

/approve

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: qiancai

The full list of commands accepted by this bot can be found here.

The pull request process is described here

Details

Needs approval from an approver in each of these files:

• OWNERS [qiancai]

Approvers can indicate their approval by writing /approve in a comment
Approvers can cancel approval by writing /approve cancel in a comment