Do the Jedi defeat and capture #DarthMaul on #Tatooine ?
Yes-
Then , perhaps, the #Sith have already won. Succeeding events would most likely cause the #Republic to split and the #JediOrder to be disbanded or even eliminated.

Maul is taken to Coruscant. Assuming he doesn't escape or kill himself, eventually he exposes Palpatine's identity as Darth Sidious.

Possibly Kenobi remains in the Jedi Order while Yoda etc agrees to Qui Gonn training Anakin away from the Temple to avoid any

"contamination" with Senate politics and a Dark Lord of the Sith who is now (probably) running the Republic

Or

The Jedi attempt to arrest Senator Palpatine, maybe even with Maul's help

Edit: This could go very wrong for the Jedi , maybe Qui Gonn and Anakin are sent away to avoid any fall out . Meanwhile the political ramifications of a Jedi arresting a senator are huge.
The Separatist movement could start much earlier putting the galaxy on the route to civil war.

#Whatif

#StarWars

However I think either the best result is if Anakin is taken away from the corrupting influence of Sheev Palpatine.
What is the likely probable result of both scenarios is that the Jedi are removed from the Republic as it's main peace keeping force in favour of the clone army. Force sensitive children are still trained but only to both develop their powers and to be taught not to abuse them. They are then invited to leave the Order on adulthood or completion of their training

Palpatine is allowed to stay in power with the Jedi closely monitoring his activity:

The Jedi Council officially bar Qui Gonn from training Anakin, so he leaves with Anakin and trains him elsewhere (with Yoda’s secret blessing). Dooku betrays the Jedi at the clone war’s climax,initiates Order 66 at the death or arrest of Palpatine by the Jedi and allows the clones to enter the Jedi Temple. Most clones deliberately miss their targets as the Jedi knew about the control chips in advance.

Eventually the Empire builds up , but its expansion in the Outer Rim is thwarted by a mutiny by the clones themselves and a Rebellion against the Empire begins much sooner, the senate impeaches the Emperor, in albeit a symbolic move, which encourages a number of high ranking Imperials to reach out to the surviving Jedi and, with the help of survivors and exiles such as Yoda, Qui-Gonn and Anakin, Palpatine and Dooku are arrested by some of their own officers.