You are overthinking this. There is no requirement that you keep an actual copy of any Form 1040-ES that you filed. In fact, no such form is even needed if you make your estimated tax payment online. All you need to do is keep track of your estimated tax payments so that you can enter them into TurboTax, as you have done. Given that the IRS has a record of your payment, they are not going to ask you to prove that you made the payment as long as what you report on your tax return for estimated tax payments agrees with the records in your tax account. Even if there is disagreement, a Form 1040-ES is not proof of payment. Anyone can manufacture a Form 1040-ES at any time.
https://www.irs.gov/pub/irs-prior/f1040es--2023.pdf
