Indeed, wheel sizes in inches are confusing and should be avoided. The reason is that the size indicated is the diameter including the tire that changes with the tire width.

ETRTO sizes gives the rim diameter in mm.

What you need is ETRTO355, there are indeed nowadays few bikes with this tire size (the Tyrell Yve can be added to the above list together with kids BMX).

According to my knowledge, Schwalbe has by far the biggest choice in ETRTO355 tires:
- Kojak 32x355
- Marathon Racer 40x355
- Marathon green guard 44x355
- Black Jack 47x355
- Big Apple 50x355
- Billy Bonkers 50x355 (its a BMX tire supposedly usable for road/urban riding, but I having had one in my hands, its a really thin tire, I wonder if its strong enough ???).

There is also an excellent (the lightest and fastest tire in ETRTO355, much better than the poor/fragile Kojak) 32x355 Panaracer Minits Lite PT but very difficult to find (never tried it, but I used the Minits Lite PT in 32x406 and its a good road tire, comparable to a Schwalbe Durano).

A Maxxis 38x355

Vee Tyre Co has several ETRTO355 tires including a 57x355 Crown Gem.

And several BMX tires which are usually around 55mm wide (don't know if any is puncture resistant enough to be used for road/urban riding?).

Tires wider than 50mm will normally not be usable with the original Birdy mudguards (its the case of the Crown Gem).

For the Birdy, the one I prefer by far is the Big Apple 50x355, its strong enough, its comfortable, reasonably fast and allow gravel use of the Birdy.