(Although I do have to eat my words here - I didn't check that Wikipedia page, and it does actually list a ~6K RISC-V core! It's an experimental academic prototype "made from a two-dimensional material [...] crafted from molybdenum disulfide"; I don't know if that construction might allow for a more efficient transistor count and it's totally impractical - 1KHz clock speed, 1-bit ALU, etc. - for almost any purpose, but it is technically a RISC-V implementation significantly smaller than 26K)
That sounds like a microcoded RISC-V implementation, which can really be done for any ISA at the extreme expense of speed.
Maybe other CPU's have it as well, though I do not have enough information on that.
This is actually kind of counter to your point. The really tiny micro-controllers from the 80s only had 224 bits of registers. RV32E is at least twice that (16 registers*32 bits), and modern mcus generally use 2-4kbs of sram, so the overhead of a 32 bit barrel shifter is pretty minimal.
There are many chips in the market that do embed 8051s for janitorial tasks, because it is small and not legally encumbered. Some chips have several non-exposed tiny embedded CPUs within.
RISC-V is replacing many of these, bringing modern tooling. There's even open source designs like SERV that fit in a corner of an already small FPGA, leaving room for other purposes.