As far as Harry's visa 'issues', there is no 'official' investigation underway by USCIS or the Dept of State. What's pending in court is a FOIA (Freedom of Information Act) request by Heritage Foundation to obtain his records. FOIA cases are civil, not criminal. So at this point he's in no danger of being arrested as an 'illegal immigrant' or for 'committing fraud'. For that to happen USCIS would have to open an official investigation and make findings that he violated the law and issue a warrant etc etc. I don't know if an investigation would suit Trump's agenda or not, and that would be the deciding factor. I know he doesn't like them, but they'd be small potatoes to him, he has bigger 'enemy fish' to fry.
IF they left due to 'visa issues' it's because there's something they don't want seen by the public if the FOIA request succeeds and are hoping that by leaving the whole thing will drop. Because Heritage will defo release those records if there's anything in there that will suit their purposes. And them leaving doesn't automatically stop that case from proceeding. Personally I don't know what could be so terrible. Everyone knows he used drugs, nobody really cares. The fact that he most likely lied about it is pretty much accepted and again, no one really cares. And if he didn't lie and they let him in anyway, so what? Plenty of 'famous' people have been let in who have used drugs and admitted it. The only difference with Harry is that he's currently on the 'wrong side' of the majority political party. If there were to be any fingers pointed it would be at the Biden Administration for 'letting a person of 'not good moral standing' in.
No, I think their return is much more likely to be for financial reasons and/or staking a claim to 'being a part of the RF' when 'in the fullness of time' it will be William in charge. I think the 'demotion' of AMW has probably scared the shit out of them and although I hope that KC has many years ahead of him, HAM may either know something we don't (hopefully not) or they're just thinking far, far ahead.
I think we can 'look forward' to HAM carrying out what they feel would be 'royal appearances' in the hopes of 'play the game, get the name'.