Does anyone know how to fix that?
Brave Support may / will need more info.
Brave Support gets a lot of reports and requests every day. In order to ensure that your issues get addressed/resolved:
[They request] Please adhere to the guidelines to the best of your ability, and use the Template shown in the Reply Editor. [No quotes, in the following links - copy and paste the link into new browser windows:]
How to submit a Bug Report:
The Brave Community webpages use a Categories and Tags - topic organization system - that assist Brave Support and Community members.
Sounds like, for your concerns / issues, you might select:
Browser Support > Desktop Support
Not sure if Office 2013 follows through with Default apps (In Windows 10 Settings, "Default Apps). Is Brave your default browser here?
Also possibly the older Office 2013 not following Default Apps in windows 10. I did test Office 2019, Opening a link in Word launched Brave.