There are a couple good resources on this. The nyt rent vs own calculator is good but also there is a great podcast episode (tailored for Canada but mostly the same in the us)
https://rationalreminder.ca/podcast/323
You are exactly right and I will add this to my post.
This calculator get most things right. As an exercise, you can try to retroactively put the numbers for the house you bought and the rent equivalent. The results might surprise you:
www.nytimes.com/interactive/2024/upshot/buy-rent-calculator.html
