This mod adds omnidirectional movement to Minecraft 1.20.1.
Since I couldn’t find a Forge version, I made my own.

Features

Sprint in all directions only (simple, right?)

This mod is designed to be used together with TACZ and Parcool+,
but it also works fine even if you don’t have those two mods installed.

TACZ Compatibility (Gun-Fu Mode)

When using TACZ, you can take advantage of Gun-Fu Mode.
If you reload your weapon while sprinting, you can perform hip-fire while running, and your movement speed becomes slightly faster as well.

Known Issue

While using omni movement, you cannot shoot while holding the W key.
This is a limitation of TACZ (or possibly Parcool), and I wasn’t able to change it with my current skill level.

However, you can shoot in a workaround-like way:

Hold a full-auto weapon
Start omni sprinting
Hold A / S / or D
Start firing
While still holding the fire button, press and hold W

This allows you to effectively shoot while holding W, but it only works with full-auto weapons (or certain burst-fire modes).
It does not work with semi-auto weapons.

That said, Gun-Fu Mode itself works even with semi-auto weapons.

OmniSprint_By Forge1.20.1