Most carbon bikes these days are pretty robust. I wouldn’t go throwing it around but you shouldn’t have to baby it any more than you would any other bike that you like and don’t want to damage.
5-6k will get you a pretty darn good carbon bike with Ultegra Di2 from most every manufacturer (except maybe the boutique-y ones). They might come with more entry level wheels than compared to the 7-8k models but they’ll still be a sweet ride, especially compared to your older, “cheap” bike.
Here’s a Specialized Tarmac in your price range as a reference: Tarmac SL7 Expert - Ultegra Di2 | Specialized.com