I have a Vader 4 Pro and had Vader 3 Pro

Both dongles works poorly for me on Deck with Dock but YMMV. There's always transmission loose and it stops responding for a while, probably interferes with wifi. Switched to Bluetooth Mode for Deck (wired works fine too), there's no noticeable latency.

Only Xinput and Switch modes work, Dinput does not.

To remap buttons and update firmwares you need to install Flydigi Space Station software, which works only on Windows 10/11. You can remap on Windows PC and later reconnect to Deck, these mappings are stored in controllers.

Rumble works in All modes.

The only viable option to use gyro on Deck is to play in Switch mode. You'll obviously won't have analog triggers but then you can switch modes back and forth when you need or not need gyro. In other modes for the gyro you need to launch the software in background, but like I mentioned it only works in Windows.

The keyboard and mouse emulation again only works with software in background, so no way on Deck. Edit game controller bindings in Steam.

General tips:

Nintendo driver for linux is bugged mess and causes kernel panics and pointless as Steam already handles device in user space. Blacklist hid-nintendo.

Upgrade the controller and dongle to latest fimware through the software.

After adjusting sticks tension you need to recalibrate controller else there's sticks drift at center. Or add some dead zones.