So how do they make money? Are they hoping to convert users to their VPN service? Or are they just trying to stay under the free tier Google API limits?
Leta is the supported search engine of Mullvad Browser which is a privacy-centric version of Firefox that integrates with Mullvad VPN. Think Mullvad Browser:Regular Internet as Tor Browser:Onion websites. So this is part of an ecosystem for their VPN subscribers.
(I'm a Mullvad customer, not Mullvad directly, but that's how I use their browser and Leta.)
In the past, Leta was a service that was only accessible to paid Mullvad users. I'm unsure when they started allowing general access, but that's initially how it made commercial sense.