Within the native Brave Wallet, FIL support is implemented using Glif's RPC endpoint C++ client. Glif is an interoperable application and toolset for the Filecoin network, including libraries, web frontends for processing Filecoin and hardware wallets, and the RPC service used by Brave.
The continued collaboration between Brave and Protocol Labs dates back several years, from early inclusion of the IPFS Companion extension to releasing a full suite of IPFS functionality in January 2021, making Brave the first major browser to natively feature a complete IPFS node.