100% - Harry wants what William gets. The fact he has complained about William getting the 'better half" of a shared bedroom at Balmoral says it all IMO. This is just another example of being unhappy he doesn't get the same as his big brother.
What I find galling is that, as has been pointed out countless times, Harry has been aware (surely) since at least 2011 that in terms of police protection his aunt and uncles have been treated differently to his father. Not because the Queen hates her younger children, not because the men in grey suits have plotted it, simply, purely because Charles is a different position than they are. He is more senior because of his birth right and because of that he is better protected because he is a higher risk and a greater, more important asset to the UK. Why Harry now acts surprised by it I do not know.
What I do understand is Harry pushing for some police protection while in the UK. In many ways I would love to see it as simple as - you quit, so you lost it, tough. But it is the protection of him and his family and to be fair, if as a country we can give Taylor Swift police outriders for her concerts here Im not hugely opposed to a few police officers keeping an eye on harry to stop the crazies getting to him (even if some of them are those Harry and Meghan have encouraged themselves) I have no doubt that a great many well known people are looked after by the police better than you and I are merer "normal citizens" are. I am sure , for example the police would respond quicker to a call (likely from a specially fitted panic button) from Zara and Mike's house than they would my house. So yes, I can understand Harry pushing for an element of police protection. What I find outrageous is him trying to dictate the level of protection - armed officers and a lot of talk about attacks on vehicles etc suggesting he wants, IMO, police outriders. Sorry, no. The police and security services decide the level of protection offered to you based on professional threat assessments, you do not demand it. That shows IMO his "demands" are not merely just about protection but about gaining equal status and "perks" (as I think Harry sees them) as his brother. For context, in one of the many reviews from 2011 onwards there was a huge drawing back on the number of armed police protection officers, not just to members of the Royal Family but senior members of the UK government and others. They replaced armed officers with officers with tasers and other more normal defence items, with armed police called in if needed. I would find it likely if even working members of the RF always get armed police protection when out and about on public duties these days, so Harry demanding it as a given right anytime he is the UK really is beyond the pale.
It is also worth remember, if he was serious about his and his family's security one would think it better not to have gone to the papers in the first place complaining he didn't have armed protection, at a time many people probably would have assumed he did. One the greatest defences most protected people have is the fact they never disclose what security they have.