The software demo was fantastic
The software demo was fantastic. That is almost irrelevant.
Demos are built to be demoed. The data is clean, the user is an admin, the workflow is the one the product does best, and the person driving has done it two hundred times. You have just watched the product in the conditions it will never see again.
What decides whether the purchase works is everything the demo skipped.
Migration: what happens to eleven years of your records, including the wrong ones, and who does that work.
Integrations: does it talk to your accounting system today, in production, at a customer like you, or is that "on the roadmap."
Exceptions: show me the order that gets returned twice. The customer with two billing addresses. The refund after the period closed.
Permissions: can the warehouse see margins? Can they change a price? Who finds out when they do?
Reporting: run the three reports your finance team lives on, from the demo data, right now.
Adoption: how many of the vendor's customers your size are still using it two years in, and can you call two of them.
Lock-in: how do you get your data out, in what format, and what does it cost to leave.
None of that fits in a demo, which is why the demo is where the decision gets made and why so many of them are wrong. Enjoy the demo. Then send the list, in writing, and make the answers part of the contract.