(docs): update force deployment condition for build docs (#22954)

previous shouldDeploy condition have not been included in deployment
condition. This variable has been updated to "forceDeployment" and
included back in the deployment condition.

shouldDeploy has been updated to check if release builds are the latest
version in its major version series.

tools/pipelines/build-docs.yml

@@ -64,18 +64,11 @@ variables:
     value: true
   - name: isMain
     value: ${{ eq(variables['Build.SourceBranchName'], 'main') }}
-  - name: shouldDeploy
-    value: ${{ or(
-      eq(parameters.deployOverride, 'force'),
-      and(eq(variables.isMain, true), eq(parameters.deployOverride, 'default'))
-      )}}
   - name: shouldRetainGuardianAssets
     value: ${{ or(
       eq(parameters.guardianAssetRetentionOverride, 'force'),
       and(eq(variables.isMain, true), eq(parameters.guardianAssetRetentionOverride, 'default'))
       )}}
-  - name: arrow.releasedtoproduction
-    value: eq(variables.shouldDeploy, true)
   - name: deploymentToken
     ${{ if eq( parameters['deployEnvironment'], 'new' ) }}:
       value: "$(FLUID_WEBSITE_TORUS_API_TOKEN)"
@@ -121,7 +114,6 @@ stages:
             echo latestPipeline ${{ variables.latestPipeline }}
             echo n1Pipeline ${{ variables.n1Pipeline }}
             echo repoToTrigger ${{ variables.repoToTrigger }}
-            echo shouldDeploy ${{ variables.shouldDeploy }}
             echo shouldRetainGuardianAssets ${{ variables.shouldRetainGuardianAssets }}
             echo publishGuardianBaselines ${{ variables.publishGuardianBaselines }}
           displayName: Show Variables
@@ -339,7 +331,12 @@ stages:
   displayName: 'Deploy website'
   pool: Small
   dependsOn: ['build', 'guardian', 'check_branch_version']
-  condition: eq(dependencies.check_branch_version.outputs['check_branch_version.SetShouldDeploy.shouldDeploy'], 'true')
+  condition: and(
+    not(eq(parameters.deployOverride, 'skip')),
+    or(
+      eq(dependencies.check_branch_version.outputs['check_branch_version.SetShouldDeploy.shouldDeploy'], 'true'),
+      eq(parameters.deployOverride, 'force')
+    ))
   jobs:
     - job: deploy_site
       displayName: 'Deploy website'
@@ -357,7 +354,6 @@ stages:
 
         - task: AzureStaticWebApp@0
           displayName: 'Deploy website to ASWA'
-          condition: eq(variables.shouldDeploy, true)
           inputs:
             skip_app_build: true # site was built in previous stage
             skip_api_build: true # api is written in js, no build needed