Most races pay very little prize money. For example, winning the KOM or Green jersey at the tour is worth $30K, a stage is $1,500. As you mentioned, all the $$$ a team wins at a race is typically pooled and divided equally among the riders and staff.
Your median Pro Tour rider makes mid-high 5 figures as a salary (I use median, since the few riders with mega-contracts really skew the average). Per the union agreement, riders must be paid at least the French minimum wage (not really an issue at the Pro Tour level except for new signings). Riders also get $$$ from any individual sponsorships (most have their own shoe contracts for example), appearance fees at post-TdF crits (anywhere from $1K-$50K a pop). Most also have bonus clauses in their team contracts for winning important races (ex. $100K for winning worlds, $75K for Paris Roubaix, etc.).
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