It was double, equal billing. And his PR was much more relatable 2000s millenial fun guy, whom everyone enjoyed.
But whether or not someone spelled out for him that eventually, when he married and had children, it would change, I couldn't say. The royals are bad at feelngs? words? IDK For centuries, they've been bad at getting everyone to play nice. I think the set of 90s 90210 was a more cohesive safe space (and I don't care what you say Jennie, Shannon banned you from her funeral). I also do think that Kate, with her close family planned on keeping Harry close and Meghan's American threw her and she didn't recover fast enough.
Still, I believe that Meghan didn't know who Harry was as much as I believe Kate didn't have William's teen beat poster on her wall and Harry didn't know that Will and Kate get first, then him and Meghan. He certainly knew he was third and before his cousins, aunts, and uncles.