Word processors for MacBook Air with macOS 12.7.6

You can rule out Microsoft based on their support commitment as described by others here. Though, Microsoft does provide an entire free, web-based implementation of Microsoft 365 with an established Microsoft account.

There is the free LibreOffice Suite that is frequently updated with feature additions and improvements. I wouldn't even give OpenOffice a side glance. LibreOffice will have a learning curve, somewhat eased by their PDF documentation, coincidentally created by LibreOffice Writer. Above the yellow Download box on this link, choose the correct distribution for your Mac (macOS: Apple Silicon, or macOS: Intel).

Just a free word-processing application that is periodically updated is Bean. It opens and saves to Word DOCX.

And if you are willing to pay for it, there is a supported MS Office clone by Softmaker which offers clone applications very much looking like Word, Excel, and Powerpoint with document compatibility.

Everything I have mentioned above works on macOS Monterey 12.7.6.

I didn't mention Apple's Pages, Numbers, and Keynote because if you never installed them prior to or on Monterey, you cannot get them now as their installation requirement is presently Sonoma 14.0 and shortly that will increase to Sequoia.

Microsoft has a policy of only supporting the three most recent versions of macOS – so if you do not already have a compatible version of Microsoft 365 or Office, it is too late to get either of those.

There are free (for now) online versions of Word, Excel, and PowerPoint. They run in a Web browser, so you can't run them when offline. They also might not run as fast, or have as many features, as the desktop versions.

Microsoft – Microsoft 365 - Use Microsoft 365 apps for free on the web

There's Pages – if you downloaded it in time. The current App Store version requires Sonoma or later.

LibreOffice will run on Monterey.

Limnos wrote:

You can also have a look at the free Open Office. To me it looks like it hasn't been updated in a while but since you are running an older system that may not really matter to you.

https://www.openoffice.org/product/index.html

FYI, Open Office doesn't get much attention ever since Oracle changed the source code license for it and gave it to the Apache foundation to manage. That is why LibreOffice exists since some of the former OpenOffice developers forked the old code. LibreOffice has seen a lot of code cleanup including from my understanding, removing most of the Java code and introducing lots of other updates.

You can also have a look at the free Open Office. To me it looks like it hasn't been updated in a while but since you are running an older system that may not really matter to you.

https://www.openoffice.org/product/index.html