Well it is literally exactly what I was asking for. :) But as you allude to the setup is not trivial and would be a bit of a project. It is useful to know about because it could help find a somewhat simpler alternative. And I will add it to my own list in case I find none.
edit:
Led me to https://github.com/polo2ro/imapbox. Which is a different take on the same problem. I am not sure if I like the email all being converted to html like this. It could be a really nice addition but somehow I feel that keeping more original-formatted emails would be wise too. It does also create for each message “A gziped version of the email in .eml format” alongside the html but I would have to look more into what can be done with that.