I am using section sizes that are not current, (they are historical sections). I have found out that I can update the section database so my sections are inputted here which I can then use to add/assign. I wanted to ask if there is a way that the section database I have updated on my computer can be used by other users in the company on their computers? I have checked and other users are unable to see the properties I have inputted when they open the model on their machines. What may be the solution here?

The details of sections are stored in some .db3 file in below location.

C:\ProgramData\Bentley\Engineering\STAAD.Pro CONNECT Edition\Sections

Program data is a hidden folder and you need to unhide it from settings. Below link from Microsoft also provide details on how to unhide a hidden folder.
https://support.microsoft.com/en-us/windows/view-hidden-files-and-folders-in-windows-97fbc472-c603-9d90-91d0-1166d1d9f4b5#WindowsVersion=Windows_10

You need to go to that location and copy the edited .db3 file and share with other users. They need to paste the same in the same folder path as shown above. Then the new sections will be read by the program.

Some related wiki can be found in below links.

 Modifying the Section Database 

 How to add a new section database to STAAD.Pro