It certainly has an impact on geography on a smaller scale if it is big enough. A moon the size of Mars would create huge tides that would impact the shores all over the planet. Large mudflats that stretch for many kilometers, connect islands to the mainland for a few hours twice per day while flooded during high tides could be very common features on your planet. Coastal cities would have to deal with tides several meters high and build accordingly etc. Of course, the smaller the moon and the further away from the planet it is, the less it impacts your planet.

Kinda true (slab-pull also has an effect but it sort of needs plate tectonics to already exist to drive plate tectonics) but that's happening in all planets, so what is special about Earth that it developed plate tectonics while Venus or Mars didn't?

How the continents look like is mostly determined by what is going on underneath the surface. Earth looks the way it does because of plate tectonics. We have several major continents with major landforms clearly linked to tectonic plates like mid-ocean ridges or mountain ranges often existing in one long line along plate boundaries. Other planets do not have plate tectonics. The topography on Mars or Venus was built primarily by shield volcanoes and erosion. I do not know why Earth has plate tectonics while Mars and Venus don't and I don't think anyone knows. It could be that the impact that created the Moon had an effect. It could be that tidal heating from the Moon's gravity helped (especially early on when the Moon was much closer). It could be that other factors were much more important and the Moon has barely any impact.

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Regarding your fictional world, how exactly did that cataclysm happen?

There are theories that Venus underwent a global resurfacing event some 300-500 million years ago, which covered the entire surface in lava and essentially erased the previous topography. Since then, Venus' surface was mostly shaped by volcanoes and wind erosion forming more or less randomly distributed highlands, which would be continents if Venus had water. If that sounds fitting for your world, you can look up Venus' topography for inspiration.

Mars has an interesting topography with the southern hemisphere being several kilometers higher than the northern hemisphere. With enough water, that would mean one supercontinent covering half the planet and one big ocean covering the other half. Why it looks that way is still an open question afaik, I have seen a theory that a big impact may have caused it. Anyway, if your god grabbed the material for the new moon exclusively from one side of the planet (quite likely, I assume the whole population that angered him lived on that Pangea-like continent), that side could become the new mega-ocean. In that case, the land and ocean in your world may have simply switched places and without plate tectonics or other major resurfacing events, they will mostly stay where they are.

If you want your world to have plate tectonics, you could look at models of Earth in the past and future to get an idea of which landforms are possible and how they could have developed over time.