A family of Microsoft word processing software products for creating web, email, and print documents.
the issue that you have that the files with a .dotm file extension are, for some reason, not being recognised by your system as Microsoft Word Macro-Enabled Templates as would normally be the case.
I agree with Doug's general assessment. Something has changed DOTM to not associate with Word.
Yes, using the process Doug explained will reassign Word to DOTM,
Personally, when I identify one problem with bad Windows file associations in Office apps, I prefer to do an Office Repair. Part of the repair process is to set all of the Office File Associations. It is much easier to do this and fix all hidden (that I hadn't YET identified) broken file associations.
I'd definitely do a repair before uninstalling Office.
Repair Office 365 / 2019 / 2016 / 2013 / 2010
Need to make sure that Word is installed correctly from the original installation CDs? You can do it by using a command built directly into Word.
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Here are some similar articles describing how to do Office Repairs for various versions of Office and Windows. Pick the one that easiest for you to understand
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Repair Office 365 / 2019-2010 on Win 10-Vista
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Repair Office 2013/2016 in Pictures (My WIKI)
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Fast Microsoft 365 repair from the command prompt
https://office-watch.com/2020/fast-microsoft-365-repair-from-the-command-prompt/
If Microsoft 365 (Word, Excel, PowerPoint, Outlook) is misbehaving, try the Repair option. If that’s also causing trouble, there’s a hidden command prompt option.
For any ‘Click to Run’ installations of Office for Windows (mostly Microsoft 365, Office 2019) there are Repair options available to fix common problems.
Among these troubles are an Office program won’t start properly or is missing from Start menu. It’s something worth trying before calling support or checking online for help.