I would take your progesterone as usual.
If you skip it, you are likely to have an even heavier bleed next month.
The morning after pill is not suitable for endometrial protection, you still need the progesterone.
However nobody needs to be having periods at all in 2025 unless they want to, and especially if contraception is an issue you may have a better quality of life by taking a combined pill continuously or a contraceptive progestin such as desogestrel 150mcg or slynd in place of micronised progesterone, alongside your estrogen.
This could have you bleed free, hormonally stable and protected against pregnancy.