Export data with polygon selection instead of bounding points

For relatively small scale usage I would use overpass or overpass-turbo, you can describe a bounding polygon as a series of co-ordinate pairs, so probably most useful if you are using the same poly again & again or it has a relatively small number of nodes. If the area is already defined in OSM then this can be used directly in overpass queries (see the documentation for examples).

I normally don't recommend Osmium directly because on some platforms there is quite a long dependency chain for compilation, and therefore it's not necessarily the tool to fix a little problem if not already in use. Most OSM ETL-style tools (osmconvert, osmosis, osmium-tool) will take a polygon file and allow you to clip a larger dataset by that polygon file. Both QGIS & JOSM allow the creation of OSM style polygon files directly. Persnally I find osmconvert satisfactory for this type of task.

My favorite tool for extracting data from osm.pbf is OSMIUM https://docs.osmcode.org/osmium/latest/osmium-extract.html And next question is where to get the polygons with boundaries? https://osm-boundaries.com/Map of course!