Why is my Mac not showing the Big Sur update in 'Software Update'?

What model year is it? The model year of a MacBook Pro is available at Apple menu > About This Mac.

A late 2013 and mid 2014 MacBook Pro can be upgraded to the latest version of Big Sur macOS 11 but no later. 

An early 2015 through 2016 MacBook Pro can be upgraded to the latest version of Monterey macOS 12 but no later. 

A 2017 MacBook Pro can be upgraded to the current version of Ventura macOS 13. 

For all of the above, see instructions in: How to download and install macOS - Apple Support

A 2018 or later MacBook Pro can be upgraded to the current version of Sequoia macOS 15. See: How to upgrade to macOS Sequoia - Apple Support

For Macs Apple used the term "update" for minor releases (e.g., macOS 11.7.2 to macOS 11.7.3) and "upgrade" for major releases macOS 11 Big Sur to macOS 12 Monterey.

You can "upgrade" to Monterey by using the instructions in How to download and install macOS - Apple Support

Be sure to backup first ( a good idea even when not upgrading).

Note however that I don't think Monterey will be enough for you to get Microsoft Office -- I think they are only supporting the 3 most current macOS versions (Ventura, Sonoma, and the current macOS 15.x Sequoia).

If you can't get Microsoft Office or can't purchase a newer Mac, some other options for Office are:

The free and very good Libre Office https://www.libreoffice.org/

or the free Microsoft Office on the web: https://products.office.com/en-us/free-office-online-for-the-web

or Google Docs: https://www.google.com/docs/about/

or Apple’s Pages and Numbers

If you're unable to upgrade your system to get an working version of Word, Excel and PowerPoint consider the free, open source alternative: LibreOffice.

It can open, edit and save MS Office files in the Office format for sharing files or its own format. Give it a try to see if it will work for you.

Also Apple's Pages, Numbers and Keynote can create the same type of documents and export them to Office formats. They can also open and edit those types of documents.

please remember it’s 10 years old and while it may still operate okay it is now considered obsolete and vintage. This means it cannot run current versions of Mac OS and perhaps some third party apps, it also means repair parts are not available.

where I’m going is to suggest beginning to plan on replacing the 2015 with a new Mac sooner than later. For those that procrastinate they often wait too long and then are stressed when they are forced to upgrade due to hardware or software failures. It’s wise to upgrade every 5-10 years if for no other reason to stay current.