I am assuming that you have Family HDHP coverage, are 55 or over (hence the $8,000 contribution which would be the limit in your case), and that you went on Medicare after April 1, 2019. I say this last thing because it is your coverage on the first day of the month that determines your coverage for the month.
April 1 - On Medicare, then only three eligible months of HSA contributions.
April 15 - On Medicare, then four eligible months of HSA contributions.
May 2 - On Medicare, then five eligible months of HSA contributions.
Assuming that you actually had 4 months of eligible HDHP coverage, then your annual HSA contribution limit (Family HDHP policy and 55+) would be $2,666.67. This would mean $5,333,33 in excess contributions.
When you enter your tax data into TurboTax and note that you contributed the $8,000 either through your W-2 or directly to the HSA (or both), AND when you indicate which months you had Medicare coverage (remember, it's the coverage on the first day of the month that matters), TurboTax will calculate your annual HSA contribution limit, and generate a message that you have had excess contributions of $5,333,33.
If your HSA contributions were direct contributions, then TurboTax will adjust (reduce) the amount of the HSA contribution deduction on line 12 of Schedule 1 (Form 1040) to reduce it. If your HSA contributions were through your employer, then the amount of the excess will be added to line 8 on Schedule 1 as Other Income. This is because the total contributions made through the employer were removed from Wages in boxes 1, 3, and 5, so any excess contributions have to be added back to income.
TurboTax will then ask you if you will withdraw the excess contributions by April 15, 2020, or the due date of your return (if extended). Since you have apparently already done so, answer "yes".
The 5498-SA you can put in your tax file; it is rare that you ever need to add anything from it to your tax return. The 1099-SA reports on distributions from your HSA in 2019, presumably to pay for qualified medical expenses. Enter this as is.
When you contacted your HSA, did you tell them that you wanted to withdraw "excess contributions"? It is important to use this exact phrase, since this permits the HSA to fill out your paperwork correctly.
In either 2020 or 2021, you will receive a 1099-SA (an additional one) reporting the excess that you withdrew. This will have a distribution code of '2' instead of '1', to show that this is the repayment of an excess contribution to your account, AND box 2 on the 1099-SA will have the amount of earnings that the excess contribution earned while it was in the HSA. You will enter this 1099-SA (even if it the second one for this year), and the earnings will also be added to line 8 on Schedule 1 (Form 1040) as Other Income.
Now, I have to added several caveats here. First, I don't know when you called the HSA custodian to request the withdrawal of excess funds. When you did it will make a difference on what year the 1099-SAs are generated.
Second, I don't know that the amount that you thought was excess was actually the correct number. Because of this coverage-on-the-first-day-of-the-month rule, taxpayers are frequently confused on what their limit is and how much excess they contributed. If you find that TurboTax reports a different excess amount than what you thought, come back and tell us.
