No, not at all. There will be NO performance loss. The Canon adapter has no optical function, but only provides the correct back focus distance required for EF mount lenses and relays the electronic connections for focus, in-lens stabilization and aperture control.
The IS functions of a EF 400 f/2.8 L IS -II or III will integrate nicely with the internal image stabilization of a R5 or R3 and result in a few more stops of IS so your usable slow shutter range will be extended. You should wind up with having a 400mm tele that can be hand held at 1/30 sec. and the improved camera performance may provide faster focusing in low-light situations.
Canon provides several EF to RF adapters at different price points with the difference being the inclusion of a control ring to control selected camera functions at the lens and/or the ability to add filters behind the lens. Optically, they are just empty spacer tubes, so unless you need the additional control ring function, the basic ($100 version) will work well for your lens.
It's important that the mechanical (2) bayonet mounts and the position of the sets of electronic contacts are absolutely correct, so it's smart to use a real Canon adapter instead of any of the "3rd party" models on the market, some of which have proven to be poor fits.
