Why don't you just try one cassette from the shop? 11 speed with the long cage shifts a lot better with the 36t cassette than with a 46t. Pretty sure I could still get a bigger or a smaller cassette as there's still some b-screw to play with. If anything, I'd expect AXS to shift better.
Because that's what I got. Anyways, there's rumours of SRAM releasing 45t cassettes with road derailleurs and gravel sized droppers.
I'd still try the 36t with the Eagle derailleur if you have the chance, it may just work.
Why don't you just try one cassette from the shop? 11 speed with the long cage shifts a lot better with the 36t cassette than with a 46t. Pretty sure I could still get a bigger or a smaller cassette as there's still some b-screw to play with. If anything, I'd expect AXS to shift better.