Procurement processes built for software handle these tools badly, because the risk is not in the contract. It is in what the tool quietly becomes part of.
Three questions catch most of it.
Where does our data go, and for how long
Not whether it is secure. Where it physically goes, who can read it, and what happens to it after the subscription ends.
Ask for it in writing. A vendor who cannot answer that in a paragraph has not thought about it.
What happens to our work if you disappear
Small AI vendors close or get acquired constantly.
If a year of your team's prompts, templates and outputs live only inside their interface, that is a dependency nobody agreed to take on. Ask what export looks like. Ask for the file format. If the answer is a screenshot, you have your answer.
Who at our end owns this
Not who uses it. Who is accountable when it produces something wrong that goes out under your name.
If that name does not exist yet, the tool is not ready to buy, whatever it costs.