proxy: subzero integration in auth-broker (embedded data-api) (#12474)

## Problem
We want to have the data-api served by the proxy directly instead of
relying on a 3rd party to run a deployment for each project/endpoint.

## Summary of changes
With the changes below, the proxy (auth-broker) becomes also a
"rest-broker", that can be thought of as a "Multi-tenant" data-api which
provides an automated REST api for all the databases in the region.

The core of the implementation (that leverages the subzero library) is
in proxy/src/serverless/rest.rs and this is the only place that has "new
logic".

---------

Co-authored-by: Ruslan Talpa <ruslan.talpa@databricks.com>
Co-authored-by: Alexander Bayandin <alexander@neon.tech>
Co-authored-by: Conrad Ludgate <conrad@neon.tech>

.github/workflows/_check-codestyle-rust.yml

@@ -46,6 +46,10 @@ jobs:
         uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
         with:
           submodules: true
+      
+      - uses: ./.github/actions/prepare-for-subzero
+        with:
+          token: ${{ secrets.CI_ACCESS_TOKEN }}
 
       - name: Cache cargo deps
         uses: tespkg/actions-cache@b7bf5fcc2f98a52ac6080eb0fd282c2f752074b1  # v1.8.0