Layers 3-4 (network, transport) are both big-endian - IP packet headers and TCP/UDP headers use big-endian format.
This means you can't have an IP stack (let alone TCP/UDP, Quic, Capn Proto) that's little-endian all the way through without breaking the internet.
Outside the webdev bubble, it's pretty much QUIC that is irrelevant - it's just another UDP based application protocol.