People who are telling you a smart trainer and subscription aren't actually wrong although it only answers your question in a round about way. I do find that 40 min on a smart trainer is much easier then on the old dumb ones and I'm getting faster in the off season.
If your carbon frame is relatively modern and even semi-aero you won't do a lot better then it for cheap unless it doesn't fit, if you're sub 20lb already then lighter also won't really make you faster. From shopping around for new bikes the best trickle down features that make a difference start to appear around 2k though if speed efficiency was my concern I'd immediately replace the wheels with something that will cost as much as the bike. On a more modern bike the biggest improvement after yourself is the wheels. Some hubs spin better, some rims are better combinations of light and aero and spokes can matter a lot as does the tires you put on them. A lighter carbon rim with lower spoke count built to a properly fast and reliable hub with Continental 5000s tires sized to the width of the rim will be lighter, spin faster and roll smoother and better then anything that comes on a 2000.00 bike. You however are the biggest improvement. Your helmet, fit of your clothes and most importantly proper positioning on the bike will make the biggest gain in speed. Having a proper fitting that sets you to an optimal position you can comfortably hold for a couple hours or more at a time especially coupled with good clothing and helmet can easily gain you 5 min or more for every hour. So you can buy more speed and a good amount but I'm not certain there's a price break bike that will just do it, just one that will give you the best rounded features that requires adjustment from there.