We don't really need another rim vs disc debate in this thread to derail the OP's question: it's all been said before and everyone is intransigent with their opinion. That being said, I am firmly in the rim-brake camp because discs contribute nothing to the joy of cycling for the type of riding I do, and actually detract from it in many ways.
Back to the original question: IMO, the cheapest way to get a really nice, new electronic rim brake bike is to source the components and frameset separately and build it up yourself or with the help of your LBS. For example, I built up a 6.5kg Giant TCR advanced SL with SRAM Red AXS, carbon wheels, integrated aero bar, etc. for about £4k just before Christmas. (A better or lighter off-the-shelf disc brake bike would cost in excess of £10k I am sure). Right now, Wiggle are selling
a rim-brake carbon frame for £600 and Planet-X,
a rim-brake Ti frame for £500. You can buy
Red AXS 12x1 for £850 (or
Force 12x1 cheaper if you can find it), add a
Rival AXS FD for £130, and you're well on your way to a complete electronic shifting bike with
nice carbon wheels for about £2.5-£2.8k.
I'm guessing the OP is not in the UK, but I suspect there are similar deals to be found in the US.