Fix and rename publish docs CI (#6108)

## Summary

Docs publish CI had some wrong paths and in general strange naming
convention, fixed both.

## Test plan

👍👍👍 Trust me

(https://github.com/software-mansion/react-native-reanimated/actions/runs/9483047831
- test run that went through)

.github/workflows/main.yml → .github/workflows/publish-reanimated-docs.yml

@@ -1,11 +1,12 @@
-name: Publish to GitHub Pages
+name: Publish Reanimated Docs
 env:
   YARN_ENABLE_HARDENED_MODE: 0
 on:
   push:
     branches:
       - main
-    paths: docs/**
+    paths: packages/docs-reanimated/**
+  workflow_dispatch:
 
 jobs:
   publish:
@@ -19,7 +20,7 @@ jobs:
         run: >-
           git config --local user.email "action@github.com"
           && git config --local user.name "GitHub Action"
-          && cd docs
+          && cd packages/docs-reanimated
           && yarn
           && yarn build