The s3 paperwork will have the information about the mental disorder, as determined by the assessing doctors. They will have been required to confirm the person needs treatment (in hospital) for the mental disorder, and that the treatment is available.
I’m no psychiatrist, but emotional deregulation and cognitive impairment, presumably as a result of the brain injury would appear to suggest a mental disorder.
MHA Code of Practice (p26) lists clinically recognised conditions which could fall within the Act’s definition of mental disorder: including “Personality and behavioural changes caused by brain injury or damage (however acquired)”
Whether it is sufficiently severe to require either treatment in hospital or now aftercare is another matter.