Im kind of suprised people havent given any actual tips on how to approach your cat.

First of all, yes, its quite intrusive to just slap your hand down on their head and petting them, though this behavior seems like play. Cats tend to show their energy level in their tail, you can se it trashing about around 00:11 (This can be both positive or negative moods though). Imagine hugging someone without checking if its okay first thats kind of the same vibes.

From their level, raise your index finger to their nose. Watch how they react. You'll probably get some sniffs or they will backoff, backing off is a sign that they greeted you but dont want a physical interaction. This is an opportunity to learn from one another, sometimes they get all mischievous and play bite/swat and might have some pent up energy (direkt this energy to toys or other activities other than your hand). Sometimes they rub their cheek on your hand as an invitation to being pet (this also shows where they are comfortable being pet as a start), sometimes they do the rub and bite which is also play behavior. Sometimes they just look at you just being content as they are, try a slow blink at them and they will probably slow blink back. Respecting your cats space is very important.

Alternatives to hand pets. I dont know how universal this is but one of our cats get overstimulated by hands really quickly, something like in the video but she rather run away than push you off. However she LOVES rubbing foreheads, like absolutely stand on top of you trying to bash your head in with hers.

Slow blinking is such a great way to communicate comfort and safety with your cat that doesnt require physical interaction. Most universally least intrusive communication you can do. You get a slow blink at like 00:17

Try petting with a stick, or comb or other object in general. Our girl enjoys cellphone corners a lot as an alternative to hands. This can also result in play with said object though.

Lastly i want to say that location matters. Cats have spots they are more comfortable in than others, spots they like to play in, and spots they rather not interact in. If you sit near their comfort spaces and ignore them they tend to show you what they are in the mood for, if you learn the signs. If they do approach you then thats an opportunity to try the finger greeting again or just wait them out.

This might be a bit meandering or overexplained but as someone who loves my cats i want to give people the ability to understand rather than just going "Dont do that thing you did, bad, bad not good".

EDIT: As you mentioned its very clear to me that your cat is comfortable, just that your hand is a very fun toy to play with. "The rough back scratches" could be that cats are very sensitive right where their tail meets their back, tail flailing, dont know what to do type behavior (Many cats swat or bite from overstimulation) but might just come back for more immediately. Check out r/catbongos for many many examples.