My projects would be small anyway but rather than having a separate microcontoller it might be a BOM reduction to just have a softcore CPU in my FPGA fabric for some physical measurement system designs.
While this sentence shows you have already considered this point, I think it's worth considering some more before diving right into this CPU soft core approach, which, if you have no experience with it, is going to be a significant endeavor.
As to the BOM, except if you are already using a kinda beefy FPGA, the kind of soft core you're gonna be able to use (and associated memory from block RAM) will be pretty limited, and almost any small MCU for a couple bucks or less will beat that, with the ease of use you already are familiar with. Compared to the FPGA, the additional cost will be close to naught (unless you're using a very small and low-cost FPGA, in which case again the soft core you'll be able to use, if any, will be very very limited.) Then all that will really matter is possibly PCB area. Although one can find ridiculously small MCUs these days (like a few square mm in BGA.)
With that said, if you are really sure you want to go this path, you'll be tempted to either use a random soft core (as some have pointed out) that could be crappy and you'll spend days or weeks to debug it, or use a vendor-provided one (as some others have suggested), which will usually lock you in to a specific FPGA vendor. Which I don't particularly recommend especially these days of shortage.
So my suggestion would be to either use one of the proven RISC-V open-source cores (you can have a look at the Pulp platform for instance :
https://www.pulp-platform.org/ ), or write your own as Brian said, but in that case, only if you have time to do it and any interest in doing it, as a more long-term project.