The current version of Pages (v11.2) requires that you have upgraded your Mac, if its hardware is supported, to Big Sur or Monterey. If you have never installed Pages v5 or later previously, then there simply is no way to get Pages v11.1 for Catalina, and you would need to consider another word processing solution. The next paragraph would not apply.
If you have installed Pages v5 or later in the past, with the same Apple ID you are using now, then it may be possible to get the last compatible version of Pages (v11.1) for Catalina. You would launch the Mac App Store, and press cmd+0 (zero) to open the Purchased panel. If Pages appears there with an update button, click it. An initial dialog will appear informing that you need to upgrade the operating system to get Pages. Do not click Cancel, but do acknowledge this dialog. It will not upgrade your Mac. Then, a second dialog may appear offering to install the last compatible Pages version for Catalina. Accept that.
Free puts you in limited availability for decent word processing applications, as developers need to eat too. As mentioned, the free LibreOffice Suite is an MS Office clone, so there is good, but not perfect document compatibility with MS Office users. Do take advantage of the PDF user guides for the individual LibreOffice applications, as there is a learning curve involved. These guides were solely created using LibreOffice Writer.
If you do not need the complexity of LibreOffice, there is the free, but limited Bean word processing application which is not entirely compatible with MS Word documents; lacks footnotes and stylesheets.