If someone asks you for something, it could be something with undefined scope or priority. An "ask" signals "this is official". Same thing with learnings: lesson is personal, learnings means ways things are changing.
Are there dumb business terms, absolutely, but these aren't bad IMO.
I don't understand what "an ask" means. I don't know what the speaker intended with it, and I wouldn't know how a receiver would understand it.
It's just communicating badly, using words with no fixed shared meaning. Or somebody too afraid to be confrontational to phrase a demand as actually demanded.
And "learnings" is just somebody too lazy to say "lessons learned".
That said, I've never considered "an ask" to have any stronger meaning than a request. If I hear "an ask", I'm assuming I can push back the same amount I would to any other request.