As I understand it, and as RLNT correctly states, the Main Secretary of State is a constitutional officer bound by state law. When voters file with her office a challenge to the ballot eligibility of a candidate, she is required by law to conduct an administrative hearing and make a ruling. She did not initiate this action. A group of voters did when they filed their complaint against Trump's eligibility.
Once the administrative hearing began, she heard both sides and said she would announce her decision. Before she announced, the Colorado Supreme Court made its ruling that Trump is disqualified by the 14th Amendment from holding the office of president. When that news broke, the Maine Secretary of State delayed her announcement, and gave both sides additional time to review the Colorado ruling submit additional filings if they wished. She then further considered the testimony and evidence, and made the finding she did.
The Maine Secretary of State is not a judge and this was not a trial in a court of law. She is a state constitutional officer who conducted the administrative hearing Maine law required her to conduct.
Regarding the "unilaterally" part, Maine law vests this decision solely in the Secretary of State. That's just the way it is. The law also provides an appeal process, such that the secretary's decision can be appealed to the state supreme court, which will certainly happen.
The election laws differ from state to state. In Maine, challenges to candidate eligibility begin with voter actions filed with the Secretary of State. From there they can be appealed to court. Colorado is different. In that state, the process for a challenge begins in court and the Secretary of State implements the decisions of the courts. In Maine too, the secretary will implement the decisions of the courts, so the end result will be the same. It's just that in these two states, different paths will be followed to arrive at the same result.
Regarding the finding made by the Maine Secretary of State, it was hers to make. Those who disagree with it have the right to appeal and argue for its reversal.
I would be surprised if any red state did such a thing. Biden is qualified to be president because he is over 35, is a natural born US citizen, and there is no evidence that he engaged in insurrection.
It is important to note that the 14th Amendment does not require someone to be CONVICTED of insurrection to be disqualified from holding the office of president. The exact language of the Constitution is "engaged in insurrection." The Colorado district court found Trump engaged in insurrection. The Colorado Supreme court upheld that finding. And now the Maine Secretary of State also so found.
The practical effect of all this is the US Supreme Court will likely take up this question soon. On that, it seems all parties are agreed. They want this question to be heard and finally resolved by the US Supreme Court. Whatever the US Supreme Court ruling may be, it will end all lower court and administrative proceedings and apply the same in all states.