"words can be interpreted differently"... "I do not agree with what you quoted earlier"

It doesn't matter; you don't have to agree with me or not agree with me. I don't make the rules. I started to put another example and realized, I'm all "scenario'd" out. I can't keep copying IRS info here. And we both stated the earnings are going to be subject to income tax if there has not been a Roth account for at least 5 years, even if the purpose is an exception to the Penalty for early withdrawal.

I put this, already: "Earnings distributed for First Time Homebuyer is possibly excluded from both tax and penalty (it's subject to the 5-year account existence rule, as noted above, for the income tax part)." It is always excluded from the penalty, but would be subject to tax as income if that condition exists.

Scenario 1: Fine.

Scenario 2: "subject to penalty is 23000."

The distribution of contributions (not earnings and not conversions) are subject to neither income tax nor penalty, at any time ($20,000). That's why you see bad guidance on the web for using it as a Savings vehicle for an emergency fund.

In this scenario 2 you gave, this account existed from 2016 (2016-2019 contributions) up to the 2020 distribution, which is not 5 years. Taking $13,000 would be subject to penalty as early contribution and taxable as income, but gets the penalty exception up to $10,000 for first time home buyer. So, $3,000 is penalized = $300. $13,000 is subject to tax.

If this account had existed one year prior, there would be $3,000 subject to tax and no penalty.

I think this is where you are stuck; see if this helps (with my emphasis):

https://www.fool.com/retirement/plans/roth-ira/5-year-rule/

"1. Your first contribution

The first five-year rule states that you must wait five years after your first contribution to a Roth IRA to withdraw your earnings tax free. The five-year period starts on the first day of the tax year for which you made a contribution to any Roth IRA, not necessarily the one you're withdrawing from. So if you contributed to a Roth IRA for the first time in early 2020 but the contribution was for the 2019 tax year, then the five years will end on Jan. 1, 2024.

If you don't meet the five-year rule, that doesn't mean all of your withdrawals will be taxed. You can still withdraw the amounts you contributed without being taxed, because the money you put in was an after-tax contribution. Only the growth of the account is potentially subject to income tax.

However, this rule comes as a shock to some people because it supersedes the well-known rule that you have to wait until age 59 1/2 to take retirement account withdrawals without taxes and penalties. That means that even if you're over 59 1/2 when you withdraw, some of your withdrawal could get included in taxable income thanks to this five-year rule. You won't owe the 10% penalty in that case, but you'll still owe tax on any withdrawals above the amount contributed."

I think this horse might be dead. I hope my final edits make sense.

I sure hope that helps.