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There are a number of inaccuracies in Cesare Maccari's painting. Wikipedia notes that the arrangement of the chairs was of parallel rather than radial as depicted. Did Maccari accurately depict the shape of the chairs of the senate of Republican Rome? And, regardless of their accuracy, what are the chairs called that are depicted here?

The chairs are called curule chairs.

This painting is a romantic painting. It is anything but accurate. What it shows is how Victorians thought or would like it to be. Roman senators brought their own curule chairs to the meetings of the senate. Or more accurate: their servants brought them.

** I'm not sure if they sat on benches or brought their own chairs. If meetings were held outside the senate house, they definitely brought their own chairs. Inside the senate house they likely sat on benches, but I did read they brought their own chairs

Compare a curule chair with those on the painting. Vastly different. Reason for the shape of this type of chair is the toga. You can't sit properly in a normal chair wearing a toga. It would crumple and look bad. In a curule chair you have to sit upright, which shows the toga in its proper folds.

Today on toga parties people usually wear bed sheets wrapped around them. That's not a toga. A toga is a long garment, about 6 meters long, with rounded edges on one side. You have to properly wear it, and it takes time to dress up in one. Only Roman citizens were allowed to wear them, and they only wore them on special occasions, as we would wear a smoking. (Which is far more comfortable to wear.) Roman senators would wear them very often, most other people only on formal occasions. You wouldn't wear underwear with a toga, as going to the toilet would be next to impossible. A tunica was often worn under it. (Cato the Younger was notable for wearing nothing under his toga. He did it out of nostalgia, and it was frowned upon.)

• https://www.wikihow.com/Make-an-Authentic-Roman-Toga

Senators sat in U shaped rows (front, left, right) to the speaker, in order of seniority. What you do not see is the https://en.wikipedia.org/wiki/Laticlave, the broad purple stripe on the toga and tunic that only senators were allowed to wear. Senators wore a broad stripe, knights (equites) would wear a narrow stripe.

• https://en.wikipedia.org/wiki/Angusticlavia

The Wikipedia article about Roman senators shows the picture you asked your question about, with this remark:

It is worth noting that idealistic medieval and subsequent artistic depictions of the Senate in session are almost uniformly inaccurate.

According to the article Seating Space in the Roman Senate and the Senatores Pedarii by Lily Ross Taylor and Russell T. Scott in Transactions and Proceedings of the American Philological Association
Vol. 100 (1969), Roman senators sat on benches. The authors provide this description of the interior:

The interior is 25.63 X I7.73 meters with an entrance from the
Comitium about 4 meters wide. The central aisle measures 5.40 meters
in width and about 2I meters in length from the door at one end to the
raised suggestus at the other, and is covered, except for reserved
areas 2 meters long at either end, by a marble intaglio pavement. On
either side of it, running back to the lateral walls of the building,
are three stepped platforms, each approximately I9 meters long, the
two lower each m. i.8o wide, the upper on the right of the entrance m.
2.05 wide, that on the left m. 2.58 wide. On these platforms must have been the portable seats for the senators that Von Gerkan, Bartoc-
cini, and Bartoli all assumed to have been chairs. But in the Republic
and, as far as we know, in the Empire too, the senators regularly sat
on benches, subsellia.

Archaeologists Lesley & Roy A. Adkins, Handbook to Life in Ancient Rome also say:

Senators sat on benches (subselli) down the long sides of the building...

The use of curule chairs was a privilege generally reserved for consuls:

Cicero's position as presiding consul was in a curule chair on a
tribunal at the other end of a central aisle. Frequently the consul in
charge was accompanied by his colleague who was also in a curule
chair; if both consuls were absent, the urban praetor would have
occupied the curule chair.

Source: Taylor & Scott

In a footnote (13) to the above, the authors add:

Caesar, like Augustus and his successors, was permitted to have a
curule chair between those of the two consuls (Dio 43.14.5). Claudius
in senatorial trials sometimes left his curule chair and sat with the
senators (Dio 60.I6.31).

Adkins & Adkins state that, during the republic,

Curule magistrates (praetors, consuls, censors and curule aediles) had
the right to sit on a special chair (sella curulis) as a symbol of
their office.

I do not know what the seating actually depicted is called (seems to be based on a church pew) but the curule seat or chair which the consuls used is not depicted in Cesare Maccari's painting. The Wikipedia article has this depiction:

Curule chair, sella curulis, Museo Borbonico, vol. vi. tav. 28. Source

The late republic / early empire funerary relief below shows a curule chair.

Funerary relief representing a curule chair. Marble, Roman artwork, 50 BC–50 CE. From the Torre Gaia at Via Casilina (Rome). Attrib/source: Palazzo Massimo alle Terme [Public domain]