in general, i think engaging with star wars from a place of realpolitik and political analysis is a fun thought exercise, especially with the canon and legends lore fleshing out the world a bit beyond lucas's archetypal story. there's a whole swath of authors who have written books and comics for adults that all take the premises of the movies seriously, the work of james luceno jumps to mind, so you can choose to dig into that lore and take it seriously as well.
the politics of the saga are related to but greatly simplified from our reality, and there is much that can be said about the way that the galaxy is designed, from george's viet cong inspired rebellion to his prequels era citizens united and bush era executive overreach. i think it's a mistake to take the jedi's role in government too seriously, as they are kind of a hand-wavy organized militia answerable to the legislative branch (and later executive during the war).
they're both a symbol of how the system works at its best and its worst. under the flourishing galactic republic, they're ideal ambassadors of peacetime diplomacy, whose arrival at a conflict resolves it using negotiation and limited force, before those conflicts sprouted into inter-system military engagement. but under sidious, they're arguably willingly misused to enforce peace on a wider scale, due to sidious's design of breaking the galaxy with a civil war.
i see many, many takes that say that the jedi should not be involved in politics at all, but i really think that's missing the point. you can take how they are being used as like a health test of the body politic, they're an epiphenomenon dependent on the republic as a whole. by the era of the prequels, they were a tool of an age that no longer existed, a more civilized one, where conflict could be resolved locally.
should they not have participated? as george has said many times, they were in a bind. would you act to save civilian lives from an invading army of droids who didn't care for or actively sought collateral damage? could you live with yourself if you had the power to help but did not? it was doomed from the beginning, they were in a trap and about to die, but is it better to fight or run away?
anyway, i got slightly off topic. engaging with star wars politically can be a fun and meaningful exercise, which even academics are not immune from the lure. here are a few articles that i enjoyed reading, if anyone is interested:
Charles, M. B. (2015). Remembering and restoring the republic: Star wars and Rome. Classical World, 108(2), 281–298. https://doi.org/10.1353/clw.2015.0014 (link)
Conor Casey & David Kenny (2021): How Liberty Dies in a Galaxy Far, Far Away: Star Wars, Democratic Decay, and Weak Executives, Law & Literature, DOI: 10.1080/1535685X.2021.1991610 (link)
Rackaway, C. (2020). Star Wars: The Fascism Awakens: Representation and its Failure from the Weimar Republic to the Galactic Senate. Studies in the Social Sciences, 1(1), 7-22 (link)
have at them and enjoy :)