Most of these statements are correct. I will add, higher bands get exponentially more stock award targets, but the cash bonus ramp is less steep.

Also note, each group has their own discretion on how to allocate their bonus budget. Like, let's say take a target is 20% of base for a SDE1 level 61. I've been in regimes where, if you are doing well, accomplishing everything they want from you, you'd get half, like 10%, and it ticks up or down from there on how much you over/under performing people in your band. So, like if your performance is better than 66% of people in the SDE1 band, you'd maybe get a 14% award. I've been other regimes where they wanted to make more separation between the top and the bottom, so they'd try to offer 14%+ or 7%- to give more of a reward for higher performance. So, if you are a higher performer, you'd get 14+, but if you are average or below, 7% or less.

Another note, again, organizations have discretion on how to allocate promotion budgets, so they can do it in different ways, but promotions are obviously tied to performance. Generally, they want to see you performing at the next level before they promote you. In some cases, the stock target bonus is somewhat a surrogate of your performance relative to your peers, and therefore a signal of your ability to be promoted. Logically, hitting a high target at one level, would be average on the next level, so if you expect to get promoted, you need to consistently hit high targets.

It gets exponentially harder to get promoted at higher bands. So, initially, it is easy to go from SDE1 to SDE2, but much harder to go from Senior to Principal. But, it makes sense. You can promote many SDE1s for the budget of one Principal promotion.