I feel like that his lack of perversion to pissing people off would come in handy if he is intellegent to know when. I think his lack of strong will will eventually fad as he gets more use to ruling however that may be limited. I do find that his personality seems to be he takes time to make decisions and is open until he makes it at which case good luck trying to push him out of it. This seems to be his main weakness he can’t make that decision quickly and enforce it. So it certainly would be interesting
Not that I disagree with what you wrote but, with a lot of a negative PR he got, it is really hard to tell something definite about his personality or ability to rule in a long term. Inability to make decisions when under pressure cost him his throne and life but if he survives, there is no real need to make instantaneous decisions.
He did piss off quite a few top figures but the main reason for their aggravation was his attempt to force them to learn at least elementary parade ground drill: all these people had been generals who never saw the service (common practice of the previous reigns was to give high military ranks to the court figures who never served in the military). Of course, this was unnecessary humiliation but OTOH none of them asked to have that rank revoked. These people were not a real danger: they’d be ready to kiss any ass and they did not have any real power behind them.
The problem was that he was too assured in his divine right to rule that he did not bother to provide an effective backup. Empress Anne created 2 new regiments of the Guards who had been loyal to her. Elizabeth took care of pampering the Guards to such a degree that they practically ceased to be military units (no drill, no discipline, unrestricted drinking and debauches, no participation in the 7YW even if some individuals did serve in it). CII also was very careful about maintaining loyalty of the Guards. Basically, only Paul did something serious about introducing discipline in these troops and we know how it ended anyway, during his reign social composition of the Guards changed: unlike earlier reigns, only officers were from nobility). PIII was openly offending the Guards and was planning to send them to war agains Denmark but his support base was limited to the tiny contingent of the Holstinians whom he did not even risk to deploy in the critical moment (as an option, he could flee to Rumiantsev’s army and this would mean a guaranteed defeat of the plotters).
So if PIII successfully evades the coup, it means that he has enough brains and presence of mind to keep ruling. If he is backed by a
real military force than the Guards can easily be reformed: the troublesome elements are sent to the army regiments and replaced with the loyalists (Paul did something of the kind), number of the Guards regiments increased with the new ones packed by the potentially loyal people and the old regiments losing their priority status (Paul made the newly-created Cavalerguards the most prestigious unit of the Guards), etc. So in that area we at least know how things could be done.
The rest is much less clear. We do not know how he would handle the Polish issue and in OTL Catherine’s actions there at least formally triggered her first Ottoman War. Would Peter fight such a war and if yes, then when and with what result? What would be his future internal and foreign policy and how would it be impacted by his fascination with Old Fritz?