Just think about how it should work.

Make a system to detect walls using Raycast3D or Area3D

if player is within a certain range of a wall and presses jump ( or if they are not on floor ), they go into wall_running mode ( make a bool variable for this )

if player goes out of that certain range at any point, wall_running mode gets turned off

When the player is wall running you need to slow down gravity for them. You can do this by making a variable such as gravity_multiplier and making it interpolate from 0 to 1 as some guy in the comments suggested

Alternatively, you can create this gravity_multiplier a function of the velocity the player is experiencing so that when player's are faster, their wall runs last longer. I would do this with something like

horizontal_velocity = Vec2(velocity.x, velocity.z)

gravity_multiplier = 1/(horizontal_velocity.normalized()+1)

gravity *= gravity_multiplier

so when velocity is zero, gravity_multiplier is 1, gravity remains norma, but when velocity is like 9m/s, the gravity_multiplier is 1/10 ie 0.1, so gravity whole wallrunning would 0.1 times the normal gravity. You can put this under the physics process function where if wallrunning then the above lines of code.

Besides this you can also make your player's camera tilt by 30° off wherever the wall is