Obviously, it is fine for passengers of a private boat to go swimming/diving/spearfishing.
But what about the case when the boat is anchored half a mile from the shore and everybody on board leaves for a swim, including the skipper?
(I am not discussing obvious safety concerns here)
I took a look at the Australian Boating Handbook and did not see anything about a case like this.
Any country laws are fine for starters, though I am mostly interested in Australian specifics.
The Act, Regulations, and the Boating Handbook do not address this directly, but as a practical matter, boats are left empty on the water for extended periods. Of course, if anyone's safety is endangered the last skipper (or the owner if the last skipper cannot be determined) will be held responsible.
If we do as you say and disregard the "obvious safety concerns", then there is nothing explicitly stated in maritime law on this general issue. This does not mean that doing so will always be legal (eg domestic laws may impose additional requirements on such practices). Of course, this would be very different if your question asked about permanent abandonment which is considered under maritime law.
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Although outside the scope of your question, the complete legal picture is that there are very real safety concerns that make it unlikely for the skipper to allow such a course of action to take place. Under Maritime Law, the skipper is legally responsible for the safety of the ship and its crew members at all times. Leaving the boat unattended could be considered negligent if it leads to unsafe conditions or hazards. This will be a question of fact.
If it is found that this compromised the safety of those on board, then the skipper will need to justify why they believed they acted in the best interests of all those on board.
I'm not aware of any such requirement for leisure boaters. There's no requirement for a permanent anchor watch for leisure boaters and thus, this is generally not implemented. It's very common that the crew anchors off a beach and then uses the dinghy to visit the beach and eat out in a restaurant there.
Obviously, that is reasonably only possible in calm weather and when the skipper is certain that the anchor will hold. And don't forget to switch on the anchor light if you intend to return after nightfall only! Besides the imminent danger of somebody colliding with your boat, it could otherwise also be difficult to find your way back.
I personally order an anchor watch whenever I'm not 100% sure the anchor will hold or the weather could change. And I was lucky I did so a few times already (as the anchor did not hold). I'm usually sailing with a group of very responsible friends, and they understand when this is necessary, even if it means taking shifts for the whole night. I can very well understand that anchor watches during a holiday trip with a crew mostly interested in swimming and going out are not particularly popular and thus the skipper might be tempted to trade safety for fun.
