Just to add to what @JonL mentioned, TypeSense is a self-hosting service. So you will need to install and host your own server for the database (index).
Whatever hosting you use must be very fast, reliable and always available.
Algolia takes care of all this hosting for you.
So maybe you could save some money hosting TypeSense yourself but not sure if the savings might be worth all thr trouble.
But it’s really nice to have that option and will be good to see if someone can provide some price comparisons.