The instructions are handled by microcode ROM on Pentium-M. They both (and some other microinstructions) jump to a common dummy routine, which seem to only raise exception. Unfortunately the code contains a lot of weird opcodes and flow bits (EOM or Fl2/Fl3), so purpose is unknown at this moment.
I have not found udbgrd on Core/Yonah CPUID 6E8, just udbgwr.
References
github.com/712ccca9-0294-4352-b994-457977fd46b8↗ - github.com/chip-red-pill/udbgInstr/tree/main/paper↗ - Intel Atom Goldmont udbgrd/udbgwr description
Additional note on related 0F 0C
On Goldmont, int paper arxiv.org/pdf/2501.12890↗ authors state: "During our analysis of Goldmont’s public microcode, we discovered a new undocumented instruction with opcode 0f 0c. This instruction maps to an intriguing microprogram with a complex control-flow graph that contains physical loads and stores to and from architectural register rax and performs port I/O, among other things. We have not yet determined what the instruction does, though we suspect it might involve some kind of inter-core communication..."
0F 0C is just UD on Yonah 6E8.