When I try to save an excel file I'm getting a "you do not have permission to save this file to this location" message. I created bot the file and excel file on the same macbook pro and this has been happening since updating to Big Sur

Where are you attempting to save the file? Make sure to only save the file within your home user folder as folders outside of the home user folder are read-only.

Do you have iCloud enabled for the Desktop or Documents folder which may be interfering? Or do you have File Sharing enabled for the folder or parent folder which may have changed the permissions (won't show up with the normal "Get Info" window)?

Make sure you are using the correct license for MS Office. MS Office will appear to work even if you are not using the correct license or if the software is not activated, but will silently restrict the ability to save files. I recently encountered this on a new install of MS Office (or it may have been an Office update that triggered the issue). I found myself logged into a MS account within Excel although I never do this. Once I logged out of the MS account within Excel and quit the Excel app I relaunched Excel which then went through a new app setup screen after which the "Save" and "Save As..." options were no longer grayed out on the File menu.

Are you using any anti-virus apps, cleaning apps, or third party security software which may be interfering?