Does upgrading to catalina or big sur take up my storage?
Normally, one OS update replaces the file contents of the previous one. While there might be some small variation in size between OS versions, I would not expect an additional 10 GB to get used up.
However, some space will be needed to download the new OS installer before it is launched.
I would install the OS, and then check how much space you have. There are disk utilities like OmniDiskSweeper that sort your whole drive by size, showing you exactly what is taking up the space and letting you delete it, if that is advisable.
You may also want to check if you have any backups of iPhones or iPads saved to your Mac, as these can take up large amounts of space.