Arduino did accept a community code contribution adding support for the .hh and .hpp extensions:
and then when that was later broken, fixed it:
I saw that as a good sign that they might be willing to support other standardized extensions and opened a feature request to add .tpp and .ipp after seeing people having problems due to them not being supported
However, I didn't get any response to that after a year. I do see Robin2's point of view but if the code is written correctly, this shouldn't be a significant burden to implement or maintain. It's just a list of supported extensions. It shouldn't matter how many items are on the list.
Since my feature request wasn't rejected, I think there is a good chance that Arduino would consider merging a pull request submitted by the community adding this functionality, but that they don't consider it a priority for the paid developers to add the feature themselves.
I do think it's quite unfortunate that there is no firm standard for these extensions. It seems like everyone just makes up their own extension. When I was doing some research as to which ones I should recommend in my feature request, I quickly got overwhelmed and gave up on it.