Dune Part Two Ending - Combat during the Holy War?

Not looking for any Dune Messiah spoilers so just hoping for some generic, broad answer rather than the specifics.

At the end of Dune Part Two, the Holy War begins which starts with the Fremen boarding what I assume are the Emporers ships (it does beg the question of how the Fremen are able to fly those ships but its not a stretch to say that some of them have off-world flying experience).

The great houses are already circling Arrakis so are there ship battles with them firing at each other? They pile tens of thousands into the ships so it makes more sense that they're going to invade each planet to conquer them (which is what I think happens) but with the great houses already being there (and I'm assuming the heads of those houses are in those ships as they have the authority to refuse Paul) is there a space firefight that happens as the ships don't look to be weaponised?

It's only a small detail but was curious.