Sync skills from tools repo to specs repo

Azure SDK common skills are developed on azure-sdk-tools repo and auto synced to all other repos and it's handled by sync skills pipeline. Currently this pipeline is not syncing the skills to azure-rest-api-specs repo. azure-rest-api-specs repo requires prettier formatting of the skills before it can be merged.

Required changes:
- [ ] Add prettier check for skills in tools repo
- [ ] Sync skills to azure-rest-api-specs repo.

Start by locating the sync skills pipeline in the azure-sdk-tools repository and trace how it targets other repositories. Check how skills are formatted before synchronization, then verify that azure-rest-api-specs receives the skills with the required prettier formatting and that the pipeline's prettier check passes.

Written by the indexing model from the issue text.