I mean, the Bourne films have their place, and you can see their influence on Quantum of Solace, and their very existence likely prompting Eon to want to go "back to basics" with Bond, or WB signing off on Nolan's take. But stylistically, Nolan brought a real flavor to cinema that is still being used, I'd argue more than Bourne.
You mention the shaky cam fight scenes, but that was only really used in Batman Begins. In the sequels and Inception, Nolan got away from that, favoring wide shots where you can see everything and the extravagant set-pieces being mostly done in camera clearly was an influence on Skyfall, Spectre and Fallout. You don't need much more proof than Fallout using a similar scene (armored car chase) and IMAX cinematography at the end. Giant aerial stunts on IMAX is a Nolan touch from TDK and TDKR specifically, and intriguingly this approach has proven to be more evergreen in its appeal to audiences than Avatar's 3D, which was all the rage a year later but has now faded as a selling point for audiences.