This article suggests a solution for the timeout issue you might have, when performing operations with large categories (1k+ plus products).
Prerequisites: The Stores > Configuration > CATALOG > Catalog > Use Categories Path for Product URLs option is set to Yes for your store view.
Steps to reproduce
Category is saved successfully.
After five minutes of saving process, the 504 gateway timeout error page appears.
The process takes longer than the server’s configured timeout.
Disabling the Generate “category/product” URL Rewrites option will remove all category/product URL rewrites from the database, and significantly decrease the time required for the operations with big categories.
Turning this option off will result in permanent removal of category/product URL rewrites without an ability to restore them.
To disable the Generate “category/product” URL Rewrites option:
bash bin/magento cache:cleanor in the Commerce Admin under System > Tools > Cache Management.
Now you can proceed to adding products to categories, or moving categories with a large number of products, and these operations will take much less time and should not cause timeout.
Automatic Product Redirects in our user guide.