For example, Musk repeatedly mentions a six-month trip. No, it is 9 months, at best.
He talks about transporting 100 colonists for those 9 months, 6500 hours, in a ship with the room that an airliner uses taking that many with their baggage across the Atlantic Ocean, up to 9 hours.
Might they not need food, water and, maybe, air for 9 months? The airliner pumps air through on the way. It collects its sewage, to deliver there. Maybe a pressure suit for when they get there? Change of underwear?
By NASA standards, Starship has room for at most 17 crew for such a trip. That is if you know they all get along, or don't care how many kill one another on the way. More practically, 8 is probably the limit.
Probably you need to send ships in pairs, so they can be swung on a cable between ships' noses for centrifugal gravity. That way their bones don't dissolve on the way. Will 1/3g be enough? Nobody knows. But it had better be.
It is a good plan to send uncrewed cargo ships ahead of time with what they will need there. You probably need at least five of those per colonist ship. With on-orbit fueling, that amounts to ~80 Superheavy launches, 10 for each colonist.
Will Starship be rated for launching crew? Maybe you need a couple of Falcon/Dragon launches, besides, for each Starship-load of 8 colonists.
So for a million colonists, you need ten million Superheavy launches. At 10 launches/day, every day, that is 3000 years. Maybe breeding colonists in situ would be faster? Because over 3000 years, some will die. (Hopefully not all at once.) How many do you need to launch just to keep numbers from falling? Maybe later ones can move into dead colonists' pressure cans, so need less cargo?
But a million colonists is very far from enough to be self-sufficient. No microchip manufacturing, no biochemicals, no Cybertruck. So you still need all the cargo launches, 10 every day, century in and century out. Hopefully the colony produces enough (movies?) to pay for that, because you can't bring them back.
So, no, there will be no SpaceX Mars colony. But promoting it keeps Tesla stock price inflated.