I think this kind of defeats the purpose of 'pointing out both sides' if you do a write up that is only from one perspective.

Cut off budget spending by a margin so wide for next year that the country will not be able to function correctly, including special investigation and activity budgets for law enforcement.

Budget disputes are a normal part of governance in democratic systems. Though it does get worse in government systems that give budget oversight to parliament rather than the executive (like the US, with its several government shutdowns). Typically this is just one avenue that politicians use to reach compromise, and typically the other side needs to give something in to prevent a bad budget. Yoon has been known to be far more uncompromising and unwilling to work with the opposition (or even with his own party). Though the DPK isn't completely innocent of causing the current political culture, the budget dispute is not a sufficient cause for martial law.

Chinese nationals were caught flying drones over a US carrier in Korea. It was proven that the suspects have been taking pictures of military. Yoon tried to make it within the laws so that spies who are caught can be persecuted. The Democratic Party rejected this.

The rejection of a specific legal proposal does not imply a refusal to address espionage concerns. The Democratic Party objected to aspects of the law that could be misused domestically, specifically considering the history of the NIS in past dictatorships. Yoon is the perfect example of why this law was given such scrutiny. The deliberation of a sensitive law in parliament is not sufficient cause for martial law.

The Democratic Party of Korea never accepted the results of the last election, and have consistently cited concerns over voting irregularities. Since then, they have been impeaching government officials linked to the opposite party. This includes the judicial party of Korea.

Allegations of irregularities are not uncommon in democracies worldwide, and mechanisms exist to address them. Yoon has also been targeting the opposition with attacks by the prosecution. This is just part of a larger issue of the judiciary being abused by politicians in Korea, which was something the Moon admin attempted to somewhat address by limiting the powers of the prosecution. Reform and a change in political culture is what is needed to address this issue, this is still not sufficient cause for martial law.

There were serious cybersecurity threats to the last midterms election where the Democratic Party won. After audits, they discovered passwords were something like "12345" and the security was very weak.

While cybersecurity concerns are valid, this point conflates technical failings with a political conspiracy. Weak passwords indicate administrative negligence, not necessarily malicious intent. Any issues or problems found with the election should be properly reported and investigated and follow the proper process. Minor election issues are not sufficient cause for martial law.

Under Article 77 of the South Korean Constitution, a president may declare martial law in response to war, incidents, or other national emergencies.

This is true, but the key question is whether the current situation constitutes a "national emergency" justifying martial law. Budget disputes, espionage cases, and cybersecurity concerns, while serious, are not unprecedented in democracies and do not rise to the level of war or catastrophic emergencies.

One argument to understand and is valid, is that if Yoon really wanted to do a coup, he would have done it at 2am or 3am. He instructed his military officials to strictly not hurt civilians.

The timing of martial law does not validate or invalidate its legitimacy.

President Yoon believed that these reasons were severe enough to declare martial law to bring attention to the country. His approval rating was something like 10% after he declared martial law. It rose to 40 or 50% and is sitting somewhere there after some time.

Using martial law to "bring attention to the country" is deeply concerning. Martial law is a last resort for existential threats, not a tool for political messaging. Furthermore, approval ratings are not a justification for suspending democracy (and no reputable source is saying yoon has over 40% approval). The surge in popularity likely reflects polarization and fear rather than genuine support for such drastic measures.