Wow, thank you so much guys for looking into this!
TLDR: I’m all set now, case solved 
Exactly these steps, yes.
Yes, I use a clipboard manager. It turned out to be the culprit - as soon as I’ve disabled its auto-transformation stuff and added Hook to excluded apps just to be safe - everything started working just as it should.
Maybe it’s worth adding some note on using third party clipboard managers there, too. A funny thing is that I’ve already had exact the same situation with some different app, and spent unreasonable amount of time investigating 
Many thanks again!