I think there's possibly some confusion creeping into things with the OP having mentioned "Arduino".
Can code be run on a specific core of a Pi and can that be dedicated to running code controlling and interacting with I/O ? Ultibo seems to allow that and I am sure it could therefore be done under Raspbian though I have no idea how to do that.
Can the code running on that core interact with code running on other cores ? I would say very probably, though again I have no idea how one would achieve that.
Creating the code to run on that isolated core should be easy enough; it just has to be able to run on an isolated core when it runs, and one needs a means to get it on to that core. Again ... no idea.
Nothing actually "Arduino" there so far, but it's giving the Pi Arduino-like capabilities in the sense of the OP's post as I read it.
The second part of the OP's post seems to suggest using the actual Arduino IDE to create the code which runs on that isolated core and that's likely possible too. I am not convinced it would be necessary, but could see why it might be a nice option to have.
As ghans suggests; that would involve writing a library so when the source code in the Arduino IDE is compiled it produces an executable which can run in the isolated core and the downloader would need to get that executable into the core. RasPiArduino seems to have covered much of that but it would all need to be bashed into shape and probably needs stuff adding.
Another alternative is for the Arduino IDE to produce executables for some other micro or Virtual Micro, download that into the core, and have the isolated core emulate that.
It's all a lot of work but likely worthwhile to some. I'd start with getting a core isolated, running code in that, figuring out how to interact with that core when running. Then move on to how to create code for it, and finally supporting it in the Arduino IDE.
Want someone else to do it ? I'd suggest suggesting a RISC-V emulator running in the isolated core, and propose RISC-V as an Arduino IDE target. See what the 'RISC-V fanboys' can deliver