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Try these supported checks and workarounds:
- In the affected document library, verify the library open behavior again: Library Settings > Advanced settings > Opening Documents in the Browser. If files are opening or downloading unexpectedly, this setting may need to be changed and saved again.
- Use Open in app from SharePoint instead of clicking the file name:
- Select the file in Documents
- Select More
- Select Open > Open in app
- Make sure the OneDrive sync client is installed and running, and that Files On-Demand is enabled. Open in app depends on both.
- If the file still downloads instead of opening, download it locally and test whether Windows opens it with Excel:
- Select the file in the library and choose Download
- Open the downloaded file from the Downloads folder
- If needed, right-click it and use Open with to choose Excel
- If the issue is only with direct links, appending
?web=1to the file URL opens the file in the browser as a workaround.
The available context does not provide a specific SharePoint Online fix for .xltm files only, but it does support checking the library open setting, using Open in app, and testing the file locally to isolate whether the problem is with SharePoint handoff or the local app association.