SharePoint excel error - A problem occurred while connecting to the server. If the problem continues, contact your administrator.

If you receive an error "A problem occurred while connecting to the server. If the problem continues, contact your administrator." while opening or editing Microsoft Office files (common with excel), use the below steps to troubleshoot and fix the problem.
This applies to all SharePoint on-premise (2007, 2010, 2013, 2016, 2019) and SharePoint Online (Microsoft Office 365) versions. Not actually a SharePoint problem, but an MS Office desktop client.

The problem is mostly user specific, device specific to be precise, and occurs while editing files.
While opening the excel, users may see a message like Server Read-Only - The document was opened from a server in read-only mode.

Troubleshooting and fixes

1. Check "Web Client" service is enabled and in running state.
Start --> Services --> Web client --> Properties --> set startup type to Manual --> Ensure its in running state.
2. Clear Office cache from your device (laptop/desktop). Reboot if necessary.
Path varies based on installed MS Office version, but something similar to C:\Users\%username%\AppData\Local\Microsoft\Office\16.0\OfficeFileCache
3. Verify SharePoint permissions - Ensure the user has minimal edit/contribute rights to the file.
4. Verify SharePoint Document Library setting "Require documents to be checked out before they can be edited ?"
SharePoint Document Library --> Library Settings --> Versioning Settings --> check out settings.
5. Delete the file from SharePoint document library and re upload. This fix works for many users.
6. Restore moved document - if you moved the document from one library/folder to another, try restoring to original location and check the behaviour.
7. If you created a Z: drive using "Add a network location", option, try deleting and recreating it.

Some additional troubleshooting tips which may help

1. Clear browser cache/history.
2. Reboot the machine.
3. Check the behaviour from a different device.
4. Try adding the link to trusted sites from browser.