Security implications of Lock Screen vs. Sleep vs. Log Out vs. Shut Down for physical access
Shut Down

Shutting down your computer is better than all the other methods. A shut down computer has less surface area to attack.

Who is the Attacker?

If the attacker is a nation state, well funded, or highly motivated, then the difference between a computer that is asleep, logged out, or locked is likely insignificant. For all these states, the computer is booted with the storage accessible to at least one process.

If the attacker is one of the above, then physical access will be enough to compromise your computer.