"Apple Silicon" is a literal truth. The silicon design, the microarchitecture, is theirs, not ARM's. The architecture, this includes the ISA but also many other things that have to be taken into consideration in CPU design (exception model, consistency, virtual memory, virtualization,...), is ARM's. They simply don't want to tie their brand to ARM's, which is fair enough, Apple's brand is much more valuable than ARM's.

Regarding the push for a 64-bit chip, I've heard the exact opposite. Aarch64 (64-bit ARM) was an ARM design without a customer, Apple were the first to buy into it. I've heard that many said it was a premature jump, and there was a lot of scepticism within ARM that they'd be able to sell it (this happened when ARM was selling mobile designs exclusively, with no intentions of getting into servers). Still, they went ahead with it, and was an unexpected success.

It’s easier to just tweak some system registers than to do that (and indeed this is how Apple implements their proprietary “in-silicon” features).