Funding != developing
The trade off is clear to everyone: firefox defaults to Google search.
No other strings attached as evidenced by firefox's better support for ad and track blocker extensions.
Discussion
A search powered by sats instead of advertisements (like DVMs) won't be a default in Firefox, or likely even considered, while there is funding from Google. Mozilla has explored other options, but I still think Google is the largest source. It is certainly influential to development.
There is no guarantee your search is not being tracked unless you take active adversarial measures.
Changing the business model from ads to pay-per-query might improve the incentives, but it offers no guarantees.