In my story, a group of scientific explorers go on a expedition to a planet, and I don't know if it should be a super continent because of the diverse life there could be. There are deserts, forest, savannahs, and mountain ranges with snow. Would creatures be as diverse in these if it was all connected or across oceans on different continents?
While oceans make very effective isolation mechanisms, there are others. This will be not so much the physical effect of, say, very high mountains as the incompatibility of habitats.
As a plain grows colder, the farther it gets from the equator, the fauna and flora will shift. Perhaps clinally, so that in theory genes could pass from artic to tropical regions, but the tropical and artic subspecies could not interbreed directly.
Then there are difference of the habitats such as grass grazers who can not live in the swamp because the footing is so uncertain, and arboreal monkeys that can not leave the swamp's trees for the grassy plains.
An enormous variety is possible.
Sure. Even if a Pangea like continent complicates a bit the atmospheric circulation and the precipitation distribution, you still have differences in elevation and solar irradiation which account for variation in local climate.
With different climates come also different life adapted to it.
You don't need to look very far for a real life example. Only a few thousand years ago you could (with some minor humping over ice and a brief swim) walk the majority of the way around the planet from South Africa to the southern tip of South America, from 68 degrees South to 77 degrees North. Even considering only the present day, Africa/Eurasia forms what is by any measure a supercontinent that is 14,000 km from the Cape of Good Hope to the Taymyr Peninsula, and 14,600km or so from Dakar to the Bering Strait, and has been in essentially that position for 30 million years. Yet no shortage of diversity in climate, ecosystems, or biology.
It depends on what kind of diversity of life you are talking about, and exactly where your super continent lies on the planet - ie, does it straddle the equator, or does it run north to south, etc.
We have gotten very unique species of animal for isolation in places like Australia, or of course, the classic example of the Galapagos islands. As has been mentioned by the others here, mountains, other landforms, and just distance in general can bring about biodiversity. If you are not aware of it, I recommend looking at the Youtube series "Alien Biospheres" by Biblaridion, as it is fantastic, and part of his imagined history on an alien world is on a super continent.
For a less scientific example for what you can do with a super continent, I recommend looking at Brandon Sanderson's Stormlight Archive, which takes place on the stormswept super continent of Roshar, and has amazing biodiversity. While the very large series is fantastic, this video gives a great introduction to what you'll find more useful in making an interesting supercontinent:
(Invicta, Welcome to Roshar | The Stormlight Archive - Lore Primer) https://www.youtube.com/watch?v=xL4M7Yx0SSE