Hi Richiee,
Welcome to Microsoft Community.
Based on the description, it seems like some users will face some issues when they open a document in local Office apps from a SharePoint site.
Before you check following details, please make sure you and your colleagues are having this issue when using SharePoint Online, if you are using SharePoint Server like SharePoint 2013, we are sorry to convey that forum engineers here focus on SharePoint Online and have limited experience or test resources on SharePoint Server. The related community is office-sharepoint-server-itpro - Microsoft Q&A.
I did some tests and here are the expected behavior. See also: Check out, check in, or discard changes to files in a SharePoint library - Office Support (microsoft.com)
1.Site owner created a workbook and checked it in.
2.Site member Mia Gray opened this workbook in local Excel app and clicked Check out to be able to edit the workbook locally.
3.Mia Gray edited the workbook normally. When the workbook is synced and clicked close button, Excel will pop out a box saying Do you want to check in. When clicked Yes, it will ask for version comments. Please note, do NOT click on Keep the document checked out after checking in this version.
4.Other users will be able to check out the workbook and edit it to check in normally.
Here are some other details we need if you want to further troubleshoot the issue.
1.Similar behavior for a document but from your description, it seems like the issue only happens on Excel workbook. Hence, please create a new workbook in the same library to narrow down if the issue is related with some other permission settings about the workbook.
2.As all Checked-Out files will show a signal in the Document Library, may I know if you or Mia Gray herself/himself will see the icon from the Document library when Mia Gray got the error 'File is already checked out to user 'graym'?
3.As you mentioned the issue will happen again just few moments after Mia Gray reuploads a workbook, the issue may be more related with the way Mia Gray check in the file, so please follow the same steps below after Mia Gray reuploads this time. Also, ask if other user following above steps will encounter with the similar error message like Mia Gray.
4.For this 'graym is Mia's log in, which she is currently logged in as. She has used Internet Explorer, Chrome, and Microsoft Edge and all are having the same issue', as you mentioned Mia Gray only opens the file locally, can she have a try to check-out file>edit file>check-in file only via browser? This helps us to narrow down the issue to the SharePoint side or the local Excel app side.
Feel free to post back.
Best Regards,
Mia