Do permanents that are also a 4/4 creature because of [[Bello, Bard of the Brambles]] trigger creature ETB effects from things like [[Warstorm Surge]]?
Yes, but only when they enter the battlefield for the first time.
If you cast an eligible enchantment or artifact and Bello is on thr battlefield, then, as long as it's your turn, they enter the battlefield also as creatures.
When it becomes your turn and these permanents are already on the battlefield, but now become creates, they do not trigger ETB effects.
If they would trigger ETB effects when becoming creatures, then all zone changes would also apply, such as taking control over a creature an opponent controls.