I know I can connect the loose cable from light switch to light fixture, but what do I do with that extra cable coming down to the outlet? Previously this was a fan/light combo with remote that had two loose three conductor (with red wires) cable coming from the light switch to fan installed by previous HO.
In electrical we don't just throw wires around.
Rules for cable routing
We start at the service panel and we run a cable from there to the first point-of-use (aka "outlet": that's a switch, receptacle etc., sometimes a lamp but there are special rules required if we do that).
From there (often, not always) we run another cable to another outlet (again: switch, receptacle, etc.)
It's a daisy-chain: from panel to outlet 1 to outlet 2 etc.
It's perfectly OK to have branches/tees: so outlet 3 could have its cable go to outlet 1 (it doesn't need to go to outlet 2).
The cable layout cannot have loops, though. Two separate chains coming from the breaker (or branched off a string) cannot rejoin. If they do, they must be carefully separated in the box. No wires from either side can touch, except the bare safety ground wires.
Your answer depends on the routing of the 2 branches you'd be joining
So now, you must either follow the wires from the switch, and the wires from the outlet... or else make some educated guesses about what they're all about.
In particular, if turning the power on causes both sides to be energized even though they're not connected yet, that means they shouldn't be connected because that would be a loop.
On the other hand, it's possible one side is entirely dead and has no route back to the panel. In that case one side needs to get power from the other. Maybe the old /3 cable carried always-hot for the onward circuit + neutral + switched-hot for the lamp.
If it's a fan-rated box, please run /3 cable to it.
I get you don't want a fan, but many people do. The next buyer of your home might be one of them. Having /3 cable from the fan to the fan-rated box will mean that person doesn't have to bust out drywall later to reinstall what you removed.
If the box is not rated for fans, don't bother; no fan should be there.