Use Nominatim for geosearch
If we adhere to the Usage Policy, why not?
It shall not be hard to implement -- adding a new parser in the components/search.service shall be sufficient. It can be then configured (enabled) via the searchProvider param in HsConfig.
The Nominatim API is described here: https://nominatim.org/release-docs/develop/api/Search/
Hm, the biggest road block would probably be the auto-complete search. Never mind, it was just an idea from JiKa.
There are also commercial alternatives. Most of them have a free tier which may be suitable for us in like 99 % cases. See https://www.geoapify.com/pricing/ or https://rapidapi.com/GeocodeSupport/api/forward-reverse-geocoding/pricing . An app would specify an authorisation token anyway, so if some HSL app would need more geocoding search, it can go into a paid plan as needed.
JiKa installed Nominatim locally for us to use (only with data of Czech Republic).
https://osm.dpz.vukoz.cz/nominatim/search?q='Hrčava'
Description of the API: https://nominatim.org/release-docs/latest/api/Search/