Best way to filter data by street width?

width= is not usually tagged, although one may easily measure it on imagery. Even if it is, there are many measures of it (ie whether to include parking and hard shoulder), that not even the uncommonly (at this scale) used width:carriageway= may be reliable enough. Width of carriageway (meaning the traveled lanes only) for a certain number of lanes (lanes=) depends on the design speed (reflected in the legal maxspeed= in operation). The entire roadway (whole paved area) needs to include hard shoulder, which although often assumed in highway=motorway (will need to exclude those without by shoulder!=no) may be under-tagged in other roads as shoulder=. You may also want to think about whether to include short sections of widening for turn lanes at intersections if this detail is present at your country being worked on, or evaluate a continuous length of main lanes only (this is better pre-processed afterwards I guess, as an outsider).

Overpass is obviously easier when working with small areas, or if you don't want to download and set up a local data file. The Overpass query would include combinations of [highway=motorway] (think you want to separately query for =trunk and =primary using different criteria), (if:t[lanes]>=3), (if:t[maxspeed]>=100) (need to use (if:number(t[maxspeed])>65) for mph units in USA), etc.

One official blog post: https://dev.overpass-api.de/blog/numbers.html