Most of his story we knew from Phantom Menace was all pre-Empire and the story that came to light with the Clone Wars has him in exile for a long time (spider legs in a garbage hole) and then as he is brought back to mental health (via Mother Talzin) and physical health (via robotic legs), he spent the rest of his days as kind of a freelance gangster. With he and Savage Opress wiping out the leaders of the Dark Sun syndicate forming the Shadow Collective, and the subsequent takeover of Mandalore / defeat of Pre Viszla / Maul head of the Mandalorian Death Watch -- I guess it's open to interpretation if Maul did all this for his own profit and power, or if it was solely a revenge path just to reel Kenobi in because of his affection for Duchess Satine Kryze. Obi Wan had a big ol jedi-boner for Satine, and (Spoilers abound, Duh: )
Maul winds up killing her in front of OWK's eyes shortly after Maul takes over the Death Watch.
The timeline of Maul appearing in the Solo movie is only about 10 years after Palpatine and Vader-by-way-of-Anakin teaming up at the end of Revenge of the Sith, and that is really where the Empire started. In the movie, Maul talks about Qi'ra returning to Dathomir (Maul's home planet, also home to his now-dead apprentice and former asskickinBroheim Savage Opress and the Nightsisters) -- No one on Dathomir is any really friend of the empire nor the Siths. They had a complicated (sometimes partnering but never trusting) relationship with Count Dooku / General Grevious and the Separatists -- Dooku's main assassin for a time was Asaaj Ventriss (a nightsister) and then Savage Opress was offered as a replacement after Dooku and Asaaj had a violent split. Dooku eventually orders an army to Dathomir and wipes out almost all of the Nightsisters.
Sometime inbetween the timeline of the end of Solo and the before the storyline of RogueOne/NewHope, Maul finds out Kenobi is on Tattooine (this would be somewhere in the window of Luke roughly being a 10-15 year old) -- Maul goes to Tattooine to face ObiWan out in the desert at night and Kenobi kills him for good this time.
So, my take (based on what we know via the
Clone Wars and
Rebels series, as well as speculation I've read otherwise ) is that Maul was not before, nor ever really part of the Empire, and the same goes for Crimson Dawn. Crimson Dawn is likely another crime faction, like the Maul-lead Shadow Collective. They do horrible stuff and they are legit "bad guys", but distinct from and not part of the Palpatine/Vader-centric Empire.
I really can't recommend the animated Clone Wars and Rebels enough. I went from movie-liking Star Wars nerd into these a couple years ago -- They were on my radar for a long time but I wanted to wait until my boy was old enough to watch them with me. They're great -- the backstory provided and context really help understand the otherwise forgettable plot presented of the abortion-worthy Attack of the Clones and Revenge of the Sith movies.