Not exactly what you are looking for, but lutris does support itch.io. The way it is implemented, it won't list the bundle contents, but only games that have been added to your collection from the bundles, to avoid cluttering your interface / hide other games you purchased.

Itch has its own launcher which has a native Linux version, you can find it on Flathub: https://flathub.org/apps/io.itch.itch

Although it doesn't get many updates anymore, feels like it's on maintenance mode. It supports installing both Linux and Windows versions of games and even launching the Windows version with Wine, although without any DXVK/VKD3D options, it's kinda bare-bones, but for the generally simple indie games on the platform it usually works fine.