Form 8332 is not required for 2021 in your situation, since you also had physical custody of the children more than half the nights of the year. If you were not in agreement, and both claimed the children, the IRS would award the dependents to your ex because the first tiebreaker is who had custody the longest.
In fact, you can't use form 8332 to “split” the tax benefits of a dependent, and the "special rules for children of divorced or separated parents" do not apply to you this year, because you are both “custodial parents” in the eyes of the IRS.
Whichever of you paid more than half the overall household expenses for the year can claim HOH status, if that person also claims at least one qualifying child dependent. It only needs to be $1 more than half. If you split the expenses exactly evenly, then no one can claim HOH because exactly half is not more than half.
The person who paid more than half the expenses is not necessarily the person who earned the most money, because money might be been spent on other people outside the household, or put into savings, and not spent on maintaining the household.
If your spouse was the person who paid more than half the household expenses, your spouse can't file HOH unless she also claims at least one child as a dependent. As I mentioned before, the special rules for children of divorced or separated parents, that allow one parent to claim the child as a dependent (using form 8332) and the other parent to use the child to qualify for HOH don't apply to you in 2021 because you both had physical custody more than half the year.
https://www.irs.gov/publications/p501#en_US_2021_publink1000220904
