Looking for input from those who have been sterilized but still get their period

I’m looking into getting a tubal ligation but I know that I will still get my period since my ovaries aren’t being removed. I’m curious if anyone knows (either from personal experience or just general knowledge) if I will be able to continue using/be prescribed my birth control after a tubal ligation for the sole purpose of managing my periods? They are debilitating and I currently don’t get my period due to birth control, but I’m worried that since I technically won’t be able to get pregnant after a tubal ligation that an OB won’t fill my BC just because I’m using it to minimize period symptoms. If anyone has any insight on this, please let me know!

EDIT TO ADD: wow, I cannot thank everyone enough for the overwhelming amount of support, well wishes, and further education on my options from everyone who has commented!! Thank you all so much for being so kind and helpful, I truly appreciate each and every one of you so much!