A baseband is a really fancy specialized SDR. Most are based on arcane VLIW DSP architectures like Qualcomm’s Hexagon or Samsung Marconi - you’ll usually have several DSPs handling the different physical layer channels, and then some coordinating DSPs doing L1 channel mixing and timing (in 4G and 5G, various logical and transport channels are muxed into the same physical channels).
Then a set of higher level processor cores (usually referred to as CP, sometimes still a DSP but often a general purpose application processor like ARM) will handle the MAC and above. There will be occasional fixed function blocks for some common protocol functions, but generally it’s less “analog magic” in the way people think when they hear “radio” and more “DSP magic.”