The police kept the protesters out, but eventually let in most members of the national assembly and their staff after checking their ID.

Martial law is about using the military to control civilian activities. The police are civilian. Their order is to maintain peace, not to interfere with people who have legitimate business at the facility. If Yoon really wanted to preempt the national assembly, he should have sent in the military earlier.

It appears that the South Korean constitution has a few provisions relating to legislative immunity:

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Article 44

1. During the sessions of the National Assembly, no member of the National Assembly shall be arrested or detained without the consent of the National Assembly except in case of flagrante delicto.

2. In case of apprehension or detention of a member of the National Assembly prior to the opening of a session, such member shall be released during the session upon the request of the National Assembly, except in case of flagrante delicto.

Article 45

No member of the National Assembly shall be held responsible outside the National Assembly for opinions officially expressed or votes cast in the Assembly.

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(from https://www.constituteproject.org/constitution/Republic_of_K... linked elsewhere in this thread; "flagrante delicto" is a legal term of art for "being caught in the act". These provisions are similar to ones found in Article I section 6 of the US constitution.).

There are reports and photos of actual troops in the building, and reports and photos of people who definitely don't look like civilian police leaving the building. I think the bigger problem with attempting to preempt the national assembly is that the troops didn't particularly want to interfere with people that had legitimate business at the assembly either.

Yeah, a few helicopters carrying troops touched down in the national assembly, but it seems they arrived too late and only waved their guns around half-heartedly. I think by the time they arrived, it was already clear which way the wind was blowing. They left soon after the vote took place.

There were videos of Assemblymen jumping the fence around the building, so it looks like the police were not letting assembly members enter.

The blockade was rather inconsistent. Some entered through the gate, some jumped the fence. Some didn't make it through at all. But If the police really wanted to block the lawmakers from gathering, they would have guarded the fence as well. The police was clearly preoccupied with controlling the protesters instead.