ci: Add merge queue triggers to CI actions (#1552)

## Description:
<!-- Describe this change, how it works, and the motivation behind it.
-->

## Is this change user facing?
YES/NO
<!-- If yes, please add the "user facing" label to the PR -->
<!-- If yes, don't forget to include docs changes where relevant -->

## References (if applicable):
<!-- Add relevant Github Issues, Discord threads, or other helpful
information. -->

.github/workflows/conventional-pr-title-checker.yml

@@ -7,9 +7,7 @@ on:
       - reopened
       - edited
       - synchronize
-  push:
-    branches:
-      - gh-readonly-queue/main/**
+  merge_group:
 
 # cancel redundant builds
 concurrency:

.github/workflows/do-not-merge.yml

@@ -3,6 +3,7 @@ name: Do Not Merge
 on:
   pull_request:
     types: [synchronize, opened, reopened, labeled, unlabeled]
+  merge_group:
 
 jobs:
   do-not-merge:

.github/workflows/gofmt.yml

@@ -7,10 +7,8 @@ concurrency:
   cancel-in-progress: true
 
 on:
-  push:
-    branches:
-      - gh-readonly-queue/main/**
   pull_request:
+  merge_group:
 
 jobs:
   gofmt:

.github/workflows/golangci-lint.yml

@@ -14,10 +14,8 @@ permissions:
   contents: read
 
 on:
-  push:
-    branches:
-      - gh-readonly-queue/main/**
   pull_request:
+  merge_group:
 
 env:
   GOLINT_VERSION: v1.53.3

.github/workflows/push-docs.yml

@@ -1,6 +1,8 @@
 name: Deploy documentation
 
-on: push
+on:
+  push:
+  merge_group:
 
 jobs:
   publish: