Hi eteb3,

I also recently cycled this way and meant to check the tagging here, so thanks for the question!

The path from North Street under the railway has a CYCLISTS DISMOUNT and a 951 no cycling sign, so IMO osm.org/way/308865423 should be tagged with bicycle=dismount to match osm.org/way/231497671 and osm.org/way/514226246

If the no cycling sign wasn't there then the "cyclists dismount" sign would be advisory, I guess the intention was to prevent cyclists from clattering their heads on the low underpass (or more cynically, to prevent them from blaming the council if they did have an off).

So it's a cycleway, until it isn't. Clear as mud, no? Either way I agree with your view.