There are a ton of word processing applications available in the Mac App Store that unless the developer has chosen otherwise, do not force an operating system upgrade from Catalina to support their current version product. Most of these vendors in the Mac App Store also have free trials from their website, so you have ample time to assess the product before paying for it. Here are a few:
- Nisus Writer Express 4, macOS 10.11 or later, $25.99
- Nisus Writer Pro 3, macOS 10.11 or later, $64.99
- Mellel 5, macOS 10.9 or later, $35.99
There are others that you can search in the Mac App Store using the term: Word processing for Mac. Once you select an entry, cilck on its website link to get to their home page and trial downloads.
It will depend on what kind of word processing you do, if you need advanced features, and whether you don't want a subscription-based product, or one that uses markdown syntax. None of these third-party word processing applications can open native Pages documents and you should verify that they can open Word documents (or RTF) exported from Pages.
I didn't mention the free LibreOffice Suite as the interface and learning curve are atrocious, despite solid Microsoft 365 document compatibility.