I have never seen any true NUC-like computer that supports ECC SODIMMs. Intel has also used the NUC brand for a much larger computer that supported laptop Xeon CPUs, but that line has been abandoned.
There have been some NUC-like computers from ASRock industrial, Supermicro and others, with either Tiger Lake or Elkhart Lake CPUs, where you could enable in BIOS the so-called in-band ECC.
All these models are obsolete. Moreover, in-band ECC is an ugly and inefficient workaround. It can be used with soldered LPDDR memories, which do not have ECC variants, but it has worse performances than standard ECC. It is not cheaper, because it diminishes the memory capacity in the same ratio as any ECC and it requires a greater die area inside the CPU for its implementation (including a dedicated cache memory for the ECC bits).
There are many mini-ITX motherboards that support ECC (but you must check carefully the specifications, even if they are for AMD CPUs). For a smaller size than mini-ITX, there are 2 choices, either expensive industrial single-board computers, which usually have the 3.5" form factor of the PCB, or one of the so-called mobile workstation laptops from Dell, HP or Lenovo, e.g. a Dell Precision mobile workstation, which are also much more expensive than an equivalent NUC-like computer.
So, if a low price is desired and an up-to-date fast CPU, you cannot have ECC in form factors smaller than mini-ITX. If paying double or triple is not a problem, there are solutions.
If you want a preassembled small computer with ECC and a mini-ITX motherboard, there are some at companies like ASRock Rack or Supermicro, but they are much more expensive than if you get the best components and you assemble them yourself.