Erroneous 2023 backdoor Roth contribution - ignored pro rata rule and failed to file Form 8606. Can anyone help?

I filed my 2023 taxes in March 2024 and a few days later contributed $6500 in after-tax money to a traditional IRA with zero balance, and then rolled it over into a Roth IRA. I made two mistakes: (1) Because I made the 2023 contribution after I filed my 2023 taxes, it's not reflected on my 2023 return - no form 8606 or amount reflected in line 20 (aside from some other stray amounts). Can I simply file an amended return with a form 8606 and call it a day? (2) I misunderstood the pro rata rule. I have another traditional IRA with a good amount of money in it. I thought as long as I segregated the before and after tax accounts, I could do the backdoor Roth without triggering tax liability. That was obviously incorrect. Do I need to amend anything on my 2023 return or do anything different on my 2024 return to make sure I've properly reported this?