From my understanding (mostly based on what I picked up back in high school), the Weimar republic was an actual working democracy (while it lasted), and that the personality cult hadn't really emerged yet until after 1933. But I realise that might be a very naïve view.
You are right that Weimar was a <mostly> functioning democracy. I think that is my point I am trying to make. The US in 2022 like Weimar in the 1920s is a functioning democracy (though the US is way better than Weimar) but there were cults of leadership back then. Nazism in the 1920s was a movement yes, but it was centered on Hitler. I am not in any way saying that Trump is another Hitler. Just that cults of personality in a democracy are very dangerous. Instead of differences by party, we have one party succumbing to one man. So in the US it's Democrats versus Republicans versus Trumpicans.
As for the personality cult beginning much earlier in Weimar - here's a paragraph from Wikipedia. The sources cites are from Kershaw's Hitler biography so they are reputable.
In June 1921, while Hitler and Eckart were on a fundraising trip to Berlin, a mutiny broke out within the Nazi Party in Munich. Members of its executive committee wanted to merge with the Nuremberg-based German Socialist Party (DSP).[100] Hitler returned to Munich on 11 July and angrily tendered his resignation. The committee members realised that the resignation of their leading public figure and speaker would mean the end of the party.[101] Hitler announced he would rejoin on the condition that he would replace Drexler as party chairman, and that the party headquarters would remain in Munich.[102] The committee agreed, and he rejoined the party on 26 July as member 3,680. Hitler continued to face some opposition within the Nazi Party. Opponents of Hitler in the leadership had Hermann Esser expelled from the party, and they printed 3,000 copies of a pamphlet attacking Hitler as a traitor to the party.[102][d] In the following days, Hitler spoke to several packed houses and defended himself and Esser, to thunderous applause. His strategy proved successful, and at a special party congress on 29 July, he was granted absolute powers as party chairman, replacing Drexler, by a vote of 533 to 1.[103]