ADHD behaviours from your list:

Eye contact/sociability, scanning environment, hyperfocus, languages/vocabulary, strong recall of e.g. song lyrics, sense of humour, talkative, debating skills, creative

Autistic behaviours from your list:

Love of routines, advanced numerical reasoning, love of puzzles, purposeful activity, recognising shapes, fondness for rules, bossy, computer skills

Both autism and ADHD:

Hyperfixations, repetitive behaviours, easily hurt, people-pleasing, tenacity, notice beauty in nature, curiosity (why?), preference for mixing with older children/adults, hyperlexia (advanced reading), anxiousness, manipulative, perfectionistic, self-doubt, self-guided learning, abstract philosophy.

I'm convinced that what we call "gifted" is just how neurodivergence presents at higher IQ levels.

What's causing it?

People with ADHD have specific impairments to the dopamine production system, so have an "interest-based nervous system": they get dopamine from stimulation, so they constantly look around for novel experiences and become deeply immersed in anything that they find stimulating. Their strong episodic memory makes it easier to recall things seen and heard (hence, song lyrics) and combined with that tendency to observe means they are more likely to link two seemingly unconnected ideas together, hence "creatively gifted".

People with autism process more sensory information than others, to the point where it can become overwhelming. Routines help reduce that cognitive load while they're processing up to twice as much visual and auditory information as others. That ability to notice every individual leaf on a tree manifests as advanced analytical and problem-solving skills.

ADHD and autism are distributed throughout the IQ bell curve, but at the higher levels, it's easy to see why we so strongly associate "genius" with people (like Da Vinci and Einstein) who had ADHD and/or autism.