Practical wideband digital beamforming for large arrays in radar applications
I've not worked on the design of such systems before, but I think your notions are on the money. Specifically, yes, beamforming arrays do have RF front ends that are replicated many times. The complexity of contemporary phased array radars is astounding in this regard; there are designs that have hundreds of individual antenna elements in them with impressive levels of control of the array response using various signal processing techniques.

And as you suspected, yes, this sort of approach is not cheap. Gigasample-class ADCs are available commercially in the few-thousands-of-dollars range, but it's possible that the custom, low-quantity RF front ends used in systems like this would dwarf that cost. Even so, radars with this sort of capability are often found as subsystems in very expensive larger systems (like a multi-hundred-million-dollar fighter jet).

As far as the backend digital signal processing goes, that's a pretty mature market that has developed over the past few decades. The main goal is processing density: getting the maximum number of FLOPS into the smallest volume. After all, such radars are often used in space-constrained applications like aircraft. Therefore, you'll see a lot of the processing done on custom FPGAs and/or single-board computers that can be stacked compactly into standardized chassis assemblies (like VPX or CompactPCI).