He doesn't give an answer about how you maintain democracy but cites his own success in using the votes of the people to strong-arm Congress so they could upend the justice system. I really hope we see genuine evidence of the corruption of the justice system in El Salvador, although I'm not sure how or when if the country's deep fabric has been so significantly altered. When could an observer understand if there is corruption and the extent of despotism - during the next cycle, when power is handed to another party/ies?
I did a scan of the "history" tab on El Salvador's wikipedia page. Here is a timeline of every time keywords like "power by force" or "murder" are used, beginning at independence in 1821:
1898 - Tomas Regalado
"revived the practice of presidents designating their successors"
1913 - Manuel Enrique Araujo (murdered)
The succeeding Melendez-Quinonez"dynasty" lasted from 1913 to 1927 [paraphrased]
1931 - Arturo Araujo
the first president elected in a free election, overthrown after 9 months [paraphrased]
1944 - General Maximiliano Hernández Martínez
ruled from 1935-39 and again 39-43 [paraphrased]; "winning back the presidency as the only candidate on the ballot"
1972 - Colonel Arturo Armando Molina
won over Christian Democratic Party leader José Napoleón Duarte) in an election that was widely viewed as fraudulent [paraphrased]
1979 - a coup d'état brought the Revolutionary Government Junta to power
One cynical-optimistic perspective is that if it takes a party strong-arming to maintain a democracy, well, then maybe it does take a revolution to maintain a civilization.
Bukele is correct in maintaining that it is unfair to compare Latin American countries to the United States in a variety of contexts - when you observe the history, noting the inverse may be true seems prudent. Looking at this timeline, I am skeptical we can fairly compare the nature of democracy itself in El Salvador to the United States. I'm also a bit skeptical of or just disappointed in Tucker Carlson for not considering all of this in context - seems like that is his job.
Another fun fact is the painting that was mentioned was of Óscar Romero:
Óscar Romero, the Roman Catholic Archbishop of San Salvador, denounced injustices and massacres committed against civilians by government forces. He was considered "the voice of the voiceless", but he was assassinated by a death squad while saying Mass on 24 March 1980.[63] Some consider this to be the beginning of the full Salvadoran Civil War, which lasted from 1980 to 1992.
Kinda see why someone would have a knee-jerk reaction to a painting of the guy getting moved by a new and extreme political leader. Skeptical again of how both Tucker Carlson and Bukele handled the topic. Here's an article about it from a Catholic news site titled "Catholics in El Salvador criticize government for moving a mural of Saint Óscar Romero." It is the second result for "bukele romero painting" on Google.