Improve output of example showcase patches CI workflow (#12609)

# Objective

Fixes #12539

Improve [this CI
output](https://github.com/bevyengine/bevy/actions/runs/8367408952/job/22909715870#step:7:11).

## Solution

- Don't stop after the first failure.
- Print the filename of the patch(es) that failed.
- Clean up an unused package install while we're at it.

Tested over here: rparrett#20

---------

Co-authored-by: BD103 <59022059+BD103@users.noreply.github.com>

.github/workflows/validation-jobs.yml

@@ -7,7 +7,6 @@ on:
     branches:
       - main
 
-
 concurrency:
   group: ${{github.workflow}}-${{github.ref}}
   cancel-in-progress: ${{github.event_name == 'pull_request'}}
@@ -299,14 +298,15 @@ jobs:
             target/
           key: ${{ runner.os }}-cargo-check-showcase-patches-${{ hashFiles('**/Cargo.toml') }}
       - uses: dtolnay/rust-toolchain@stable
-      - name: Installs cargo-udeps
-        run: cargo install --force cargo-udeps
       - name: Install Linux dependencies
         uses: ./.github/actions/install-linux-deps
       - name: Apply patches
         run: |
+          CODE=0
           for patch in tools/example-showcase/*.patch; do
-            git apply --ignore-whitespace $patch
+            # Try applying the patch, logging an error if it fails.
+            git apply --ignore-whitespace $patch || { echo "::error::$patch failed to apply."; CODE=1; }
           done
+          exit $CODE
       - name: Build with patches
         run: cargo build