CI(pg-clients): unify workflow with build-and-test (#8160)

## Problem

`pg-clients` workflow looks different from the main `build-and-test`
workflow for historical reasons (it was my very first task at Neon, and 
back then I wasn't really familiar with the rest of the CI pipelines).
This PR unifies `pg-clients` workflow with `build-and-test`

## Summary of changes
- Rename `pg_clients.yml` to `pg-clients.yml`
- Run the workflow on changes in relevant files
- Create Allure report for tests
- Send slack notifications to `#on-call-qa-staging-stream` channel
(instead of `#on-call-staging-stream`)
- Update Client libraries once we're here

test_runner/pg_clients/java/jdbc/Dockerfile

@@ -1,4 +1,4 @@
-FROM openjdk:21
+FROM openjdk:22
 WORKDIR /source
 
 COPY . .