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Does SQLite have GIS capabilities (like PostGIS provides for Postgres), or is this storing the data as traditional database primitives?
SQLite + spatial (and specific metadata tables) is essentially the Geopackage format, which can be considered the modern equivalent of a shapefile.

Which is to say, yes, SQLite has geospatial operations and they’re well supported by the open source gis stack.

This is super cool. As part of the Pelias geocoder(https://pelias.io/) we use both OSM and SQLite heavily. Currently we've written our own pbf2json tool in Golang (https://github.com/pelias/pbf2json). But creating intermediate databases in SQLite could enable more powerful manipulation of OSM data before we eventually import it.
This is AWESOME! I'm doing some volunteer work to make a map of cycling routes in my city, and using OSM data to annotate features. Having a SQLite db of all the Way tags would make my work a lot easier! Thanks!
Could this be used for reverse geocoding?