Deciding on decidability of a problem and reducing it to halting problem if not decidable

Question

Given are two following languages:

$L_1 = \{ w\#x \hspace{1mm} | \hspace{1mm} w,x \in \{0, 1\}^* \text{ where } M_w \text{ with input } x \text{ visits each of its states at least once} \}$

$L_2 = \{ w\#x \hspace{1mm} | \hspace{1mm} w,x \in \{0, 1\}^* \text{ where } M_w \text{ with input } x \text{ does not visit at least one of its states} \}$

Are the languages decidable/undecidable/semi-decidable?

The intuition tells me that both languages cannot be decidable, for the simple reason that if any of them ends up in a loop, it can never be decided whether all states were visited. Is my way of thinking correct in both cases?

I would also say that $L_1$ is semi-decidable - in case all states were visited after some finite number of steps, we could decide the language and if not, we still won't be able to say anything about it.

Is it possible to reduce the halting problem to this problem to prove that it's not decidable?

Thank you!