I don't think the via is the issue.
I see two immediately obvious issues on the layout, that should be addressed first:
1) Your antenna has no matching network. Place at least a PI in between the antenna and the switch. Someone also need to connect the antenna (and the added pi network) to a VNA, and measure it, and select the right value components. This needs to happen 100% on every PCB antenna designs, and it's not something that you can just simulate or copy.
2) I don't think the antenna layout is OK. You copied the ground plane clearances, but you didn't place the antenna in an optimal orientation.
3) Your SMA might not be 50ohm with this layout.
But even without both of these fixed, you should have some reception, which makes me think there is another, more fundamental issue with your system. Meaning that having both these fixed will improve your signal maybe 20-30dB, but two boards next to each other should 100% be able to communicate with each other, since they have something like -90dB link budget. Something else is blocking the RF completely, like timing, channel selection, software...