Here is my deal: If you know you want to buy, why not explore what would be required to do that? You could have guidance from 1-3 lenders (more opinions = better than fewer opinions!) by early next week. The lender is really the person that's going to tell you whether buying by June 2023 is do-able. Finding a house is the easy part!

And honestly, especially if you have a pretty clear idea of what you want, finding a house takes way less time than you expect. And it sounds like you are blessed by a kind and reasonable landlord. They might be willing to let you go month-to-month if it took you longer than June 2023 to find a house.

Working backwards, 45 days is plenty of time to get from contract to closed. So if you needed to be out of your rental by no later than May 30, that means you have to have something under contract by April 15. That's eminently do-able.

November to April is plenty of time to find a house to buy. You just have to decide if you are ready.

ETA: Spelling