Another option would be STM32 development board (F4/H7/etc. with ADC inputs, DAC output and enough ram) + some sensor with FM modulation input and IQ outputs (
https://www.rfbeam.ch/product?id=9, innosent.de, etc.). Note that some sensors with FM input can only perform FSK but not FMCW. Then you connect IQ outputs to ADC, and FM input to DAC. You've already mentioned TI's evaluation boards, check Infineon's BGT24 series evaluation modules too.
On a budget (need good soldering experience): take
https://wiki.dfrobot.com/mmWave_Radar_Human_Presence_Detection_SKU_SEN0395 , de-solder main MCU, find out which pins are for IQ, VCO, etc., put wires to some 32bit ARM development board.
Cheapest possible option: take HB100 module, de-solder 100uf capacitor from power, by varying input voltage you can shift it's frequency by some amount, maybe few MHz max. It would be enough to perform FSK modulation. It uses dielectric resonator oscillator for 10GHz, but by altering Vds we can shift S-parameters a little (S21 phase in parallel feedback loop), which will result in frequency shift. Voltage may by applied through dac+opamp. Performance would be not great though, because amplitude will vary, and it is limited to FSK, and there is no prescaler output to know current frequency for precise distance calculation. For a university project I would recommend buying some good evaluation board (TI or Infineon). Check if you can record data and perform some processing in Matlab or other software before buying.
These products are already reasonably priced, let's not forget that ro4350 substrate is pretty expensive, and they usually combine with FR4 into 4 layer to arrange MCU placement, which makes it even more expensive. Manufacturing cost of single tiny PCB prototype easily will cost $150+. Mass produced cheap sensors use cheap components, there is no much functionality.