Some things you can try:

Only do movement in FixedUpdate so that it's in step with the physics simulation (not really practical but an option)

Move your character with velocity instead of transform.position as you might end up inside the terrain if you move too fast horizontally into a slope.

Decrease the fixed time interval to make physics calculations more frequently per frame, this will help stop your character from going through things if it's moving too fast.

Use a different collider, either box or capsule as mesh colliders are more prone to getting stuck in things, also it'll be faster. If you're using a mesh collider make sure it's set to convex otherwise it wont collide with other mesh colliders.

Place box colliders in the terrain where clipping is likely, this will act like reinforcement for areas with an odd shape. Typically developers will place invisible walls around areas where the player isn't meant to go, that's perfectly fine so long as it's not too obvious to the player.