feat: add GitHub Actions workflow to check for PR merge conflicts (#1586)

This workflow automatically checks if a pull request has merge conflicts
with the base branch. It uses the GitHub API to query the mergeable state
and fails the check if conflicts are detected, making it easy to spot
PRs that need to be updated before merging.

Author: maxprilutskiy

.changeset/silly-lizards-jump.md

@@ -0,0 +1,2 @@
+---
+---

.github/workflows/pr-merge-conflict-check.yml

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+name: Check for Merge Conflicts
+
+on:
+  pull_request:
+    types: [opened, synchronize, reopened]
+  # Also run when the base branch is updated
+  push:
+    branches:
+      - main
+
+jobs:
+  check-merge-conflict:
+    runs-on: ubuntu-latest
+    if: github.event_name == 'pull_request'
+
+    steps:
+      - name: Check for merge conflicts
+        uses: actions/github-script@v7
+        with:
+          script: |
+            const pr = context.payload.pull_request;
+
+            // Get the PR details to check mergeable state
+            const { data: pullRequest } = await github.rest.pulls.get({
+              owner: context.repo.owner,
+              repo: context.repo.repo,
+              pull_number: pr.number
+            });
+
+            console.log(`PR #${pr.number} mergeable state: ${pullRequest.mergeable_state}`);
+            console.log(`PR #${pr.number} mergeable: ${pullRequest.mergeable}`);
+
+            // The mergeable field can be: true, false, or null (if GitHub is still calculating)
+            if (pullRequest.mergeable === null) {
+              console.log('GitHub is still calculating mergeable status. Waiting...');
+              // Wait a bit and try again
+              await new Promise(resolve => setTimeout(resolve, 5000));
+
+              const { data: updatedPR } = await github.rest.pulls.get({
+                owner: context.repo.owner,
+                repo: context.repo.repo,
+                pull_number: pr.number
+              });
+
+              console.log(`Updated mergeable state: ${updatedPR.mergeable_state}`);
+              console.log(`Updated mergeable: ${updatedPR.mergeable}`);
+
+              if (updatedPR.mergeable === false) {
+                core.setFailed(`❌ PR #${pr.number} has merge conflicts that must be resolved.`);
+              } else if (updatedPR.mergeable === null) {
+                core.warning('⚠️  Could not determine merge conflict status. GitHub may still be calculating.');
+              } else {
+                console.log(`✅ PR #${pr.number} has no merge conflicts.`);
+              }
+            } else if (pullRequest.mergeable === false) {
+              core.setFailed(`❌ PR #${pr.number} has merge conflicts that must be resolved.`);
+            } else {
+              console.log(`✅ PR #${pr.number} has no merge conflicts.`);
+            }