Use Nominatim: https://nominatim.org/
It can be self-hosted, with constant replication. There's also Photon which is a cut-down version of it: https://photon.komoot.io
It can be self-hosted, with constant replication. There's also Photon which is a cut-down version of it: https://photon.komoot.io
An in-between for OP could be something like opencagedata.com, which is still a third-party API but an order of magnitude less expensive than Google. (not affiliated but have previously explored the service)