Use Pull Request Labeler

[gpetrou]

Is your feature request related to a problem? Please describe.
Currently, https://github.com/banyan/auto-label is used which seems to be outdated and produces an action error.
For example, https://github.com/elastic/elasticsearch-net/actions/runs/8183925897/job/22388312350?pr=8053.

Describe the solution you'd like
Use https://github.com/actions/labeler instead.

Describe alternatives you've considered
A clear and concise description of any alternative solutions or features you've considered.

Additional context
Add any other context or screenshots about the feature request here.

[flobernd]

Updating the action to a better supported one is probably a good idea. However, what I can tell from a quick check, the root of the error seems to be a permission problem.

I think the action should be triggered by pull_request_target instead of pull_request and additionally needs:

permissions:
  contents: read
  pull-requests: write

The whole CI, actions, automations in this repository should be modernized at some point... For now, the client itself has highest priority, but I've put an item on my backlog.