does grammerly work with pages?

Does Grammerly work in the pages app?

Apparently it does. A recent-ish Grammarly support article here says:

Does Grammarly work in Pages? 

You can use Grammarly in Pages by installing Grammarly for Mac on your computer if you have macOS 12.2 or newer. To find out more about Grammarly for Mac, check out this article. If you use an older version of macOS, you can also upload your documents to the Grammarly Editor. 

...and it continues with the steps of how to achieve this.

They have revised the current version 1.10.0 to skip signing up, or signing into an existing Grammarly account during the installation process before it can be used. It will open a browser window with another sign-in dialog, but that too can be skipped.

It is working with Pages v12.1 on macOS 11.6.8 and the Mac requirements for this version state macOS 10.12 or later. When you open a Pages document in thumbnail view, you will see a numerical badge icon at the bottom of the gallery indicating the issues it has found with the current document, and clicking on that badge reveals options, or begins the process of stepping through the issues for you to decide on correction:

If you already have a Grammarly account, download their macOS version and try it with Pages. You might get a quicker answer to your question doing that than by waiting for a response here.