Is there a way to adjust templates based on at which heading level they are inserted?

What I’m trying to do

I have created a template, which has headings. I use this template in notes which have their own heading hierarchy. I want to make sure that the template is inserted at level 2, and then template headers are auto-adjusted to 3 and above. Right now if the template has top-level headings and I insert it in sub heading level, it creates ad new top level heading.

Things I have tried

I looked at the template syntax and also in Obsidian forum, the closest I got was this topic. But it does not have answers.

With the built-in templates, no. With Templater, maybe (but I imagine it’s a bit involved).