> SEO is the practice done by webmasters of optimizing a website to improve its visibility and ranking in search engine results.

They do this because they benefit from their site being visited or the information they are providing being noticed.

> If you are paying to use your search engine, does that mean webmasters are no longer incentivized to/will not try to improve their visibility/ranking in your search results?

I see no reason it would have that effect. It does, however, create different incentives for the search provider to improve the signals indicating page relevance since the user is the priority instead of advertisers.