unless there is a clause in the purchase contract to finance only with bank XYZ
and then
In my opinion, illegal tying arrangement. The notary would also get into trouble for that. Such things are done more subtly, as the OP described, but certainly not provable on paper.
I keep saying this over and over like a preacher. The buyer the buyer the buyer pays and chooses pays and chooses the notary. His! notary. Don’t let the seller push you around. A little mutual respect, that also creates respect. Otherwise, they think you are just dumb cash cows.
According to your description, I would be more afraid of signing the loan agreement and then selling to someone else... However, the other way around... you still have all options open once the notary appointment is over.