updating microsoft word on mac after catalina update

Microsoft Office 2019 and Microsoft Office 365 work with Catalina. Neither are free. Office 2019 is a one time payment and Office 365 is a subscription. Microsoft Office Purchase Site

Free options, although not 100% compatible with Microsoft Office include:

LibreOffice

GoogleDocs

Office Online

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Microsoft 365 is a subscription app, Office 2019 is a one off payment.

Libre Office is free, https://www.libreoffice.org

office 365 id rent so it's an ongoing expense

office 2019 is one time fee

libreoffice is free and support ms office files

Install it and find out.

If you are asking about LibreOffice, it is not 100% compatible. Not all formatting may work.