Its the third option, and no while nothing in computer infrastructure is ever truly free as theres always operational+maintenance cost as well as dev time and setup time, when nothing is at cost to the end user and the hosting provider isn’t trying to make a profit off their information then I consider it good grounds to it a ‘free’ service. I actually just posted a guide to alternative search engines over at !technology@lemmy.world , you may find it an interesting read.