Looking at wandrer.earth's rules, the highway types mentioned in my first paragraph (primary, secondary, tertiary, unclassified, residential) aren't in their list of types which require an explicit bicycle=yes|designated tag:
"If they don't have an allowed bicycle tag, ways with the following highway tags are removed: motorway, motorway_link, steps, stairs, escalator, elevator, construction, proposed, demolished, escape, bus_guideway, sidewalk, crossing, bus_stop, traffic_signals, stop, give_way, milestone, platform, speed_camera, elevator, raceway, rest_area, traffic_island, services, yes, no, drain, street_lamp, razed, corridor, busway, via_ferrata"

While it does no harm to add bicycle=yes to the primary, secondary and tertiary roads in this changeset, if wandrer.earth excluded those roads the problem may lie elsewhere.

I won't remove the tags, although there's no guarantee that someone else won't decide that they're redundant in the future.