I feel like you're really changing the definitions of these things to fit what you want them to fit. Strange New Worlds absolutely would not be called more of a crossover than a spin-off. Strange New Worlds only happened after how much people loved how the three characters were used on Discovery.

DS9 wouldn't have happened without TNG, Miles and Worf wouldn't have been on another show without TNG. The beginning of DS9 is literally dealing with storylines and character arcs established from TNG. A crossover is when you combine two things that already exist, when one show is created directly because of a prior show it's a spin-off.