Function objects, including closures, can be serializable - they are in Erlang/Elixir. You can send a lambda/closure over to another node (on another machine) to execute. It's actually one of the basic building blocks of OTP.

I assume this only works if the functions are exactly the same. It would break between different versions?

It depends. It’s possible to provide a mechanism to switch versions but as it very often is: there are dragons.

Seems like trampolining would be useful to make it interruptible while still mostly preserving the ergonomics of viewing state transitions as procedure calls

Serializable closures (even serializable continuations) are available in a number of languages, including probably most often ones which also have TCO.