I mean, let’s be honest: People do crimes even when they have no material need to do so, so you will always need some form of law enforcement, how should a solarpunk society handle this?
The same is true for a military: As long as there is no world peace or some magical way to shut the outside world out, and as long as other societies exist somewhere nearby (and in today’s world this means somewhere on the same planet), a society needs the means to defend itself… what would this look like?
The more favorable implementations I have read about typically take the form of community patrol groups. Members of the group rotate in and out, and when something goes wrong they step in to de-escalate whatever situation is going on. For more serious problems, those boil down to a community wide decision on what to do with the perpetrators.
As for military, there’s a few paths. In real life, the most ideal but least likely would be a world wide revolution that sees the end of hierarchy applied globally. At that point there would be no need for any military.
Next most likely would probably be a more dedicated form of the community patrol groups, with various populations pitching in with what they can and where they can.
Third is a geographical separation that leads to no need for a military. The best example of this is Annares in Ursula K. Le Guin’s The Dispossessed. Annares and Urras are sister planets/moons. Annares is an anarchist utopia and Urras an archist nightmare. Theoretically any nation state on Urras could decide to wage war against Annares, but waging war against a different celestial body is much more difficult than a normal war, so in practice the threat of war is not very large, and therefore the need for military is absent.