Yes, fashion. You are looking at the pinnacle of fashionable dress uniform of the time. From the same time period you can also find thousands of portraits of officers in buffcoats too for similar reasons. The buffcoat was a prestige item at the time as well, hence why it's included, and also it was fashionable.

Though, to be clear, there's nothing of that sorts really. Uniforms themselves being something that slowly filters in during the 30 YW (it was not invented by Gustav II Adolf, despite what some claim) and starts become a thing in the latter 1600s.

So, nobility and officers (fairly broadly overlapping groups) would wear whatever finery they could afford to following the fashions of the day, still very much influenced by the the Spanish court. These "everyday" clothes is what they would wear on the battlefield. Augmented with some armour, buffcoats and or breastplates usually. We are nearing the end of the practical wide-spread use of armour and the hard campaigning (aka walking around) in the 30 YW would be where most soldiers "lost" their armour. Most officers would be dressed kinda fancy (compared to the men at any rate) and wear some armour over those clothes, they'd generally not be fully armoured. Even in situations where it might be advisable. As the Swedish Intelligencer (a British "newspaper" providing information from the war for the British) reports in 1631, the king, Gustav II Adolf had to admonish his officers at the storming of Frankfurt-an-der-Oder to wear their armour.

There is, however, a remnant of the medieval armoured knights, the cuirassiers wearing nearly full (so called) 3/4 armour. For simplicity's sake imagine they are effectively fully armoured. Armed with swords, pistols and harquebuses/calivers (a lighter type of musket) in theory at least, most would have left the gun though. They are the heaviest cavalry present on the field of battle and are protected against most shot except heavier muskets and artillery. Obviously they are expensive to maintain, not in the least as they require powerful horses (that were not armoured) to carry them into battle. Thus their numbers are fairly few, but they are considered the elite of the elite. E.g. in Sweden who lacked the means the only standing unit of cuirassiers were the Adelsfana, the "feudal cavalry" of the Swedish nobility. There was a slow evolution during the 30 YW, in all armies, that fewer fully equipped cuirassiers were deployed as their chief function, to roll over other units in closecombat, became increasingly rare. The (eventual) momentum is towards a "medium" cavalryman with a sword, pistols, buffcoat and breastplate (being the main cavalry by the end of the conflict and for British people most recognisable as Cromwellian "roundheads"). Just about protected enough to be useful in battle, but mobile enough that they can perform scouting, foraging and such duties in the 99% of the time there is no battle. All this said, it doesn't exactly matter here, other than that the "fully" armoured cavalryman retains the image of being the best of the best.

Now, why is it black? To protect your armour from rust and make it look dope (there are other techniques such as "blueing" or reddened/rudded armour IIRC the terms right, am little unsure on the metallurgy parts, the names are based on the slight "dis"colouring of the armour as a result). The cuirassiers mentioned above would be (usually) equipped with "blacked" armour. The armour being covered with burnt oil, paint or varnish. The period leading up to the 30YW fashion was inspired by the Spanish court and black silk (as the most expensive kind) with gold and silver threading was the coolest thing you could wear. You can see many portraits of royals and wealthy nobles wearing these clothes. Fashion impacting military protection isn't an isolated case either (or the other way around). During the 1500s the "peascod" type breastplate was the height of fashion emulating the courtly dress that was fashionable then (the type you see on Elizabethan people with a narrowing in the waist.

So while armour and mediaeval knights were on the out, some of those ideals remained in imagery. If you wanted to show off your pageantry and credentials as a military man you had yourself painted in the appropriate style, which included horse, commander's baton and a cuirassier's armour, but yours of course was a parade armour.

Now do you wear this into battle? Yes, but not exactly. Armour is never comfortable and it'd make little sense to wear the most ostentatious parade armour to the field of battle, it won't protect better than a slightly less ornate armour. There's no good reason to stand out too much after all. As a commander you need to stay further back and no armour will protect you against cannon anyway. That said, sometimes you had to get stuck in, it was your duty as commander to brave the fire, or it was just that bad a situation. If you were of rank but needed to lead your troops in person, like Pappenheim liked to do, you'd most likely wore something like a cuirassier's armour, probably with some decoration because reasons. Curiously I can very specifically say that Gustav II Adolf would not have after 1627, he had taken a musketball in his shoulder that was never removed and he couldn't wear full armour after that. At the time of his death in battle (about the same time Pappenheim died in the same battle of Lützen no less) he only wore a buffcoat. The interesting thing here is that both commanders died in the same battle, armoured differently (most likely), but the end result was the same for both. Fully armoured or not, being in the middle of combat was very dangerous.

I can't really speak as to when the military baton appears, but by the 17th century it's a fixed feature of the image of the overall commander. It tells the viewer that this man was in charge of an army. Just as the armour and buffcoat was a marker of a military man. When king Gustav II Adolf died at Lützen at the head of his Småland cavalry he would be fighting with sword and pistols. Well if his arm hadn't been broken by a musketball at any rate only a short time before being killed (has being taken back towards his own lines when they got confused in the fog (literal) of war.

Edit: Putting in a late edit as I ran across just such a portrait and noticed something I was going to bring up but forgot.

The armour pictured in the paintings isn't necessarily real. Looking at a portrait of Johan Banér it depicts him in the typical black armour, but with chainmail parts that would be centuries out of fashion and used in a way it would never have been in practice. These portraits aren't painted "live" and include things that are allegorical sometimes, there are cases of rather fanciful faux-Roman or faux-Greek-Alexander-the-great styles too. Men like the ones depicted wouldn't have time to stand model so beyond some sketches, though there is a famous triptych portrait of Richelieu that actually is meant as a painting guide, the artist worked mostly off memory and artistic vision. hairstyle, beard/moustaches, even noses were routinely changed to fit the popular artistic styles.