I think drowning will probably break the vibe. I think a cute staggering will be enough. Maybe cancel flight automatically if player cannot manage to pull up after the staggering animation?
I'm not sure I understood the idea well.
When falling into the water, there is a deterioration in controllability with the corresponding animation and then the controllability is lost completely if the player does not take the right actions. The bird goes into the mode of being on the surface, from which it is possible to perform a second take-off. The same mode as on land or very close to it.
If that's your idea, I think it's pretty good on the whole.