Not entirely accurate, but not that wrong either when it comes to the basic shapes.

The outer garment depicted on the people in the painting is most likely the toga, a large semicircular piece of cloth wrapped around the body. As you can see in these pictures, they looked relatively similar to the artwork you linked. These were indeed rather inconvenient, which is why they eventually became formal dress and a sort of "national costume", with common people preferring simpler cloaks, or just a tunic like what was worn under the toga. One inaccuracy, however, is that the toga and the tunic under it would be mostly white/uncoloured, as can be seen in for example these two portraits from Roman Egypt, as well as a Pompeiian fresco depicting the baker Terentius Neo with wife. As you may see though they are not entirely monochrome; the purple stripes you see on the tunics of the first two gentlemen indicate that they are of the ordo equester (the second tier of Roman aristocracy; the senators wore tunics with broader stripe), unlike the more humble Neo. Furthermore, Roman magistrates (and underage children) wore a toga with a purple border or lining, called the praetexta, which I believe some of the men in the painting should be wearing. There was also a version of this outfit coloured purple and gold, which was worn in Roman triumphes. Plutarch says Caesar wore this at the festival of Lupercalia a few weeks before his assassination, but I am not sure if he wore that or a more ordinary outfit (toga praetexta) on the Ides of March. If you are interested in Caesar's personal style Suetonius claims he liked to wear the broad-striped tunic with long, fringed sleeves and a girdle.

I was going to delve more into Roman garments other than togas, but now I am getting rather tired so instead I will link to some earlier threads. I could write something about it later if you have questions. Anyway, in this thread, u/Astrogator writes about toga use in the provinces and quotes from some Roman sources noting how rarely it was worn in some parts outside of Rome, here our u/tinyblondeduckling writes about the culture and symbolic value of the toga compared to the Greek cloak pallium, and in this comment u/Taciteanus describes how cumbersome the toga was, and found an interesting passage in Plutarch about senators girding up their togas when needing mobility