(just to reiterate a point made above)
If you download it locally and process it yourself, as many as you like.
The software that is used when you type things in the search box on the OSM website is Nominatim. Depending on exactly what you want to do, you could install a local version of that to search for things. Alternatively, it might be easier to load the data from OSM that you want (e.g. roads, but not cowsheds, fences, memorials, and lots of other things) into a spatial database and search** that.
** that’s just a link to a random documentation page, but if you think about what you want I bet that you’ll find that someone has already asked the question somewhere like here.
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