I've started using Signal for some things, and it seems there is a way to export chat histories from the desktop client:
- Open the developer tools sidebar (ctrl-shift-i)
- Navigate through the 'Elements' view to the div.conversation-stack element
- Right click on that div and 'copy outerHtml'
- Past this HTML into a new file and save it somewhere
Now that file can be viewed with a web browser.
This isn't a particularly great export of course, but at least it's something.