Just to share a new finding with developers.
I've tried an open source (turned out it's not open source, just had a GitHub account for issues) editor called Photopea, it manages to open the PSD file, but replaces the font with another one. I understand that, as being browser based, it does not have access to my system fonts.
This app initially shows the text layer rasterized to keep it identical to the original, but allows you to edit the text by clicking on it, which saves the retyping and even keeps the original text colour.
A similar feature could be very useful in Affinity. When a bad text layer is clicked, ask the user if he wants to recover what is possible, keeping text, colour or font (ideally all).
Update: Actually after preloading the font in Photopea (File->Open->Font) it opens and edits the PSD file exactly as it did in Photoshop 7.0. It even handles alignment and text wrapping. I really hope this "Bad text data" error in Affinity is fixable.