You would need to contact Houzz customer service as this is a public forum that customer service does not monitor. Mostly advice on design and selection. I will say in all the years I have been a member here I have never heard of such a thing.

I do not work for Houzz, not do I know anything about their business, but that's a lot of money for a company like Houzz to spend for some photos that they can get for free. Tell your contractor to produce Houzz's current policy in writing and then verify it yourself. If he can't or if it looks fishy, get another contractor. This one isn't honest.

Complete BS high pressure sales tactics. Move on to a different contractor.

Most contractors and designers post photos on Houzz for free, hoping that they will get referrals/jobs from people that see the photos.

Makes no sense at all that Houzz would have a need to pay for photos!

Houzz locks contractors into advertising contracts that often have incredibly poor results. If they aren't letting them out of those deals, they're certainly not paying them 10K for a picture.