From Yonhap (Korea state news):
"Activities related to National Assembly, political parties banned: martial law commander." [1]
"Entry, exit from National Assembly blocked after declaration of martial law." [2]
That is what martial law is all about: pausing democratic norms to deal with an emergency. Voting, public gatherings, a free internet ... it is open season.
Is that even legal? Because if it is, that means the president can prevent martial law from ever being lifted. The whole constitution would be pointless.