Your logic states the following:
if Input.is_action_pressed('up'):
velocity.y -= 1
anim.play("RunLeft")
So, if your character is facing right, it will "RunLeft" and if your character is facing left, it will "RunLeft".
if Input.is_action_pressed('up'):
velocity.y -= 1
if anim.play == "RunRight":
anim.play("RunRight")
elif anim.play == "Idle_Right":
anim.play("RunRight")
elif anim.play == "RunLeft":
anim.play("RunLeft")
elif anim.play == "Idle_Left":
anim.play("RunLeft")
Now, that code above is probably not correct and may give you some syntax errors, but I think if you can sort through the errors and apply that same logic, it might point you in the right direction or give you a eureka moment.
(Sorry I couldn't post accurate code. I'm a little new to Godot myself and I don't have my computer on me right now to test, but I thought I'd try to help with the logic).