I'm turning a Gen3 Birdy City into a touring bike with a double chainring, and a spare 7s cassette (1,9 - 6,5m, 342%) which I might replace with an 11-32T 8s later (1,6 - 6,5, 406%).

The original crankset with a 52T ring is a hollowtech with unused space for a, internal chainring.

After adding a 38T internal ring and a two-speed Shimano Sora FD-3000 derailleur, it rests barely above the outer ring, which means I'd have to use a ~10mm spacer to move the crankset outward.

I know a square taper bottom bracket is heavier and not as efficient, but it's also cheaper.

Does someone know how wide its axle should be to fit?

Edit: Or do I simply need to get a wider BB (source)? The BB on the bike says "Driveline EX-TYPE BC1.37" "