The brain damage is not specific to drowning but is from what is called asphyxia, lack of oxygen. I've seen quite of few asphyxiated patients over the years and the end effects can be quite variable -- the brain is a mysterious organ. You've said your character is severe. He would then probably be on a ventilator in intensive care for several weeks, followed by several months in a rehab unit. The severity of his ICU course would depend upon how much the asphyxia affected organs besides the brain; kidneys, heart, and liver are commonly damaged but usually recover if the patient survives.
We don't use the term catatonia in this situation -- the term was once mainly applied to form of schizophrenia that has apparently disappeared. It is not a word neurologists commonly use.
The worst case scenario for your patient would be a persistent vegetative state--tracheostomy connected to a ventilator for breathing, a feeding tube through the abdominal wall for liquid feedings, and no meaningful consciousness. Some families choose this, most don't.
Best case would be complete recovery, which happens. If you want some defects, mild cases could have decreased metal capacity, down to the mental capacity of a toddler or so. You could plausibly make this as severe as your plot requires. So-called soft neuro signs would be things like memory difficulty, emotional lability, learning disability. Such a patient would probably also have some motor problems, maybe as mild as just being "clumsy."
Worse case would add motor problems to the cognitive problems, things once called "cerebral palsy," although we don't use that term much anymore. Mild cases would be one or both legs, more severe would include arms. Limbs have tight muscles, patient has difficulty using them. Often need crutches, may need wheel chair. Most of these patients continue to need special physical and occupational therapy help, but nearly all live at home--how independently depends upon their particular problems.
Deafness or blindness, partial or total, would not be unexpected.
Bottom line: the brain is quite variable, do what your plot needs, especially regarding personality, speech, intellectual capacity. All things are possible.
