Industry uses here two standards:
After print you may polish (fine sand) the inside of the lower rim (4mm) on the bottom- the diameter should be minimal 27.5mm (27.6 per design at 4mm and 28 for soda bottles). So if your print is only 27.2 you can reduce flow or print this (27.6/27.2=1.015) 1.5% bigger - best to check with the bottle you want as these also have some tolerances.
Screw gently the first time - use some lube or a little cream as fresh prints have high friction. If it seems too tight put the cap in hot water (45°C) so it can adapt a little to your bottle as the inside is designed to seal on top and bottom of the bottle thread.
This spout stays on the bottle until empty, for a bath you turn it upside down and squeeze and a fine stream of soap will flow into the water (also could inject directly in the faucet stream). There is no need to close the small opening as long your bottle stays upright. It also may release a little flavor from the soap into the air.
The author marked this model as their own original creation.