But Harry later tested time loops, and system somehow told him to stop messing with time.

More specifically Harry told himself to stop messing with time, Harry being part of the system.

If the computer MoR runs on is really able to compute infinite loops in one sweep, then there's no reason not to allow Harry to compute his primes.

Sure, if there isn't something that is more likely to happen given the state of the universe before the loop.

Instead something scarry happened so Harry had to tell himself not to mess with time.

That scary thing being Harry telling himself not to mess with time. What we infer from this depends on what we know about Harry and what sort of things are most likely to make him respond in this way.

So maybe it is Turing computable after all, it just have watchdogs to stop loops after some iteration.

Watchdogs are a possibility. This evidence should increase the probability to this sort of thing being the case. But not by much.