With this setup,  you can expect about 60 FPS (50-70) the majority of the time with mostly medium settings. I will say straight-up that this is a lot of work to set up; however, it is possible to get an experience that surpasses last-gen console performance by using CryoUtilities 2.0 @ recommended settings, setting the UMA Frame Buffer Size to 4 GB VRAM in bios, and installing Proton-GE, along with the adjustments written below. Additionally, I undervolted my Deck, which helps the game feel smoother. You'll also want to use Decky and the Decky FrameGen plugin (in the Decky Plugin Store) to install the FrameGen mod for Hogwarts Legacy.

Tutorials for these prerequisites:

After your Deck is setup and the FrameGen mod is installed, launch the game, set Nvidia DLSS (it's actually FSR 3) to Quality, and set the upscale sharpness to 0. Frame Generation should be set to x2. 

Enable HDR and calibrate as follows:

Set framerate to 40 FPS. (Don't worry, you will get higher FPS than this!)

All effects (Motion Blur, DoF, Chromatic Abberation, and Film Grain) should be turned off.

In the graphics settings, most settings will be Medium. Turn Material Quality on High. Then drop Fog Quality, Sky Quality, and Population Quality to Low.

In GameScope, set the frame limit to 80FPS/80Hz. Enable Allow Tearing. Finally, set the Manual GPU Clock to 1600 MHz. It seems like lowering the GPU clock a bit can help to stabilize frame times in Hogsmeade, as it is a CPU-bound game, but in my testing, it doesn't stabilize them enough to justify the drop in FPS. You can feel free to experiment with this, if you want.

For added stability, close the game, go into desktop mode, and navigate to "<SteamLibrary-folder>/steamapps/compatdata/990080/pfx/drive_c/users/steamuser/AppData/Local/Hogwarts Legacy/Saved/Config/WindowsNoEditor" and open Engine.ini. Then paste in the following at the bottom and save it: 

[SystemSettings] 
r.bForceCPUAccessToGPUSkinVerts=True 
r.GTSyncType=1 
r.OneFrameThreadLag=1 
r.FinishCurrentFrame=0 
r.TextureStreaming=0 
r.Streaming.PoolSize=2048 
r.Streaming.LimitPoolSizeToVRAM=1 

[ConsoleVariables] 
AllowAsyncRenderThreadUpdates=1
AllowAsyncRenderThreadUpdatesDuringGamethreadUpdates=1
AllowAsyncRenderThreadUpdatesEditor=1 

Please note that sometimes doors in the castle will take a second to open. In super demanding locations, like Hogsmeade, you'll feel the frametimes lagging a little, too, but they should be pretty smooth most of the time. It should also be noted that FrameGen introduces a little input lag. Most of that is mitigated with the settings above, so you should barely have any, but a tiny bit is to be expected.

This method was simply compiled and tested by me using info and research from multiple sources. I have to thank CryoByte33, Steam Deck HQ, Sam Alexander, Deck Wizard, and the lovely Reddit community for doing all of the hard work.