Additional chat-related features and issues within Microsoft Teams for Education
This is not exactly a new phenomenon for Microsoft. If you want usable data out of the Mac version of One Note, you have to click, select all, select all (again) and then copy and switch to a real document and paste. Aside from that, OneNote can give you a PDF as an export of your page. Great if you want to share a finished document, but not user friendly and hostile to data portability. Teams is worse in this respect in that the select all does not work at scale even within a chat. (I stand corrected on my previous advice here. It works for a bit, but not much chat history).
For my personal computing, I insist upon using tools that give me complete exportability and portability of my content (and in standards-based formats). Unfortunately, I don't have the ability to mandate these kinds of common sense requirements in my workplace, however I do try to encourage it.
Bottom line - users should demand that our data be easily and usefully exportable from any tool that we use. Chat is mostly text and some images/links, etc. No reason why a RTF, HTML, or XML file (with images in a directory) can't be produced on command. Or even a Word docx or an email.