Smooth Controls. Help needed

Hey there.

Does someone have an idea how to implement a movement (character movement) that feels smooth?
Let’s say my character is standing still.

As soon as I press backwards, the character starts to “slide” backwards while rotating towards the backwards direction.
What I want is that the character “rotates” in place and THEN starts to run.

When my character is running forwards and i press the direction for “Right” for example, the character immediately turns in a 45° angle, which doesn’t feel smooth.

Here’s a comparison to “Tomb Raider Legend”, The movement is smooth.

When pressing Left-Right repeatedly, the character also changes direction instead of turning smoothly.

Any tips for implementing this?

Root Motion is no option for me though.