So is Trump’s bombing campaign about to expand into a “freedom of navigation” mission?

The Suez AND Strait of Hormuz?

Possibly. I mean, this is the reason that generations of Presidents have declined to decapitate the Iranian government, despite them having been consistently horrific for close to fifty years. We've long had the ability to go in there and kill the leadership and bomb the bejeezus out of many of their military installations. We didn't refrain from doing so because no one realized how horrible the government was, or because anyone wanted them to persist. We just didn't have a great answer to the question is what results from that. Because unless you're planning on moving massive numbers of troops in country, you don't end up having a lot of control of what happens next (and even then, see Iraq).

It's not really clear what the Administration has planned for the aftermath of killing Iranian leadership, or how they intend to shape events in the region. As terrible as he was, killing Khameini doesn't necessarily mean anything good is going to happen. The regime could still hold onto power, of course - they've spent these decades repressing and obliterating any domestic challengers to their power, so there's not much strength or organization among the people to try to seize power (the Venezuela scenario, kill the leader but still stuck with the regime). Or the country could simply descend into chaos or a continual struggle between factions who never manage to resolve the conflict (the Libya scenario after Qaddafi was killed). It is theoretically possible that a new better government might arise without us actually putting boots on the ground, though it's kind of hard to see where that comes from - importing a royal relative might look appealing, but without any actual power base there there's a strong danger of falling into one of the first two scenarios.

And then, there's the risk of the conflict spreading and creating more chaotic states than just Iran. That's one of the regime's possible methods to try to stay in power. They will want to regionalize the war into Lebanon and the Gulf States, up the disruption as much as possible, so that there's more of a push for the U.S. and Israel to declare victory and freeze the status quo. If Trump just wants a scalp so that he is considered a consequential President, rather than trying to obtain any specific benefits for the Iranian people who oppose the regime, then that's a decent path to staying power for the Iranian leadership.

So, yeah - look for them to go after the straits, if they can.