How to physically connect AS3933 to 3D antenna?
You can't directly connect those two using a breadboard.  They are SMD parts, so you can't connect them to a breadboard.

You can probably get a breakout board that you could solder the AS3933 on to.  There are standard parts that should fit, though they might be difficult to find.

The CAS143 has its own peculiar layout for the connections.  You won't find a standard breakout to fit it.

The best thing to do would be to make a small PCB.  Design it with KiCad or any electronic design package you like, then have a PCB made from any of the commercial services.

If that would take too long (or be too expensive,) then you could try doing it "dead bug" style.  That's where you glue the parts on their backs and solder fine wires to the pads to connect things.

"Dead bug" looks like this:



It's rather fragile,but for a one off test of something it can work quite well.