Fix up Actions issues (Azure#31252)

* fail-fast: false

* Write-Host instead of Write-Error, judge failure from exit code

* Option 1: Continue processing when an error is written out. Nonzero exit code will fail the step.

* Undo eng/scripts/Logging-Functions.ps1

* Revert typespec-requirement.yaml

* Put ErrorActionPreference in the right place

.github/workflows/typespec-validation-all.yaml

@@ -34,6 +34,7 @@ jobs:
   typespec-validation-all:
     name: TypeSpec Validation All
     strategy:
+      fail-fast: false
       matrix:
         os: [ubuntu-latest, windows-latest]
         # shards must start at 0 and increment by 1
@@ -57,13 +58,14 @@ jobs:
 
       - name: Validate All Specs
         run: |
+          # Keep processing when errors are written. Nonzero exit will mark the 
+          # step as failed. 
+          $ErrorActionPreference = 'Continue'
+
           ./eng/scripts/TypeSpec-Validation.ps1 `
             -Shard ${{ matrix.shard }} `
             -TotalShards ${{ matrix.total-shards }} `
             -CheckAll `
             -GitClean `
             -Verbose
-          
-          # Effectively the same as ignoreLASTEXITCODE: true in Azure DevOps
-          exit 0
         shell: pwsh

.github/workflows/typespec-validation.yaml

@@ -17,8 +17,13 @@ jobs:
 
     - name: Validate Impacted Specs
       run: |
+        # Keep processing when errors are written. Nonzero exit will mark the 
+        # step as failed. 
+        $ErrorActionPreference = 'Continue'
+
+        eng/scripts/TypeSpec-Requirement.ps1 `
+          -BaseCommitish HEAD^ `
+          -TargetCommitish HEAD `
+          -SpecType ${{ matrix.spec-type }}
         ./eng/scripts/TypeSpec-Validation.ps1 -GitClean -Verbose
-        
-        # Effectively the same as ignoreLASTEXITCODE: true in Azure DevOps
-        exit 0
       shell: pwsh