Remove check-for-api infrastructure

This was a short lived, and unfortunately unsuccessful experiment on how
to catch API breaking changes. As we did elsewhere in the org, remove
the check-for-api infrastructure.

Author: tcharding

.github/workflows/rust.yml

@@ -118,18 +118,3 @@ jobs:
         env:
           DO_WASM: true
         run: ./contrib/test.sh
-
-  API:
-    name: Check for changes to the public API
-    runs-on: ubuntu-latest
-    strategy:
-      fail-fast: false
-    steps:
-      - name: Checkout Crate
-        uses: actions/checkout@v3
-      - name: Checkout Toolchain
-        uses: dtolnay/rust-toolchain@nightly
-      - name: Install cargo-public-api
-        run: cargo install --locked cargo-public-api
-      - name: Running API checker script
-        run: ./contrib/check-for-api-changes.sh