I want something more robust
An "upgrade" isn't the solution to this. Switch to a different type of bike could be the solution.
For example, if you have bought a road bike, and consider it not robust enough, you may want to swap it to a gravel or cyclocross bike. That won't be upgrade, though, it would be an entirely different kind of bike. An "upgrade" would be ditching a $1000 road bike and buying a $3000 road bike instead.
fast on the trail
The only parts of bike that affect its speed are the air resistance and tires. Before buying something expensive, first set up your riding position (mainly handlebar height and distance) to be optimal and then find out what kind of tyres are best for you and install those.
Configuring your riding position and using optimal tires will usually do far more to your speed than buying a different kind of bike.
About the only case where buying a completely new bike might be advisable is if you have an incorrect handlebar style. Generally, it doesn't make sense to install a drop bar to a flat bar bike. However, drop bars provide tremendous speed gains. So if you want a gravel bike, then I'm all for a completely new bike.
a better gear set.
You may be able to swap to a wider-range cassette before having to buy a completely new bike. It may mean using a different rear derailleur to have enough capacity, but still, the derailleur+cassette swap is an insignificant fraction of the price of a completely new bike.
I am considering carbon bikes, but I’m aware that these are much more expensive. Any recommendations for carbon and aluminum bikes up to $2,800?
Carbon generally isn't more robust, so if that's what you're looking for, prefer aluminum and avoid the lightestweight components.