It would be very helpful the ProSeries software could confirm the payment of estimated tax payments that are/were scheduled within the software.

Ain't gonna happen.  This would require that ProSeries have access to the client's bank account or to their IRS records.  I certainly would not want Intuit to have that kind of access even if they could.

I think the only true confirmation would be the IRS transcript to ensure that the money was credited to the TP's account for the proper tax year.  Yes, I have had IRS withdraw estimated tax payments and apply to the wrong year.

I would be happy if Intuit just calculated the tax return correctly without all the bugs.

The software is just the messenger that sends the banking info to IRS, it was no clue whether the payment has actually been made or not,  your client should be checking that the payment was actually withdrawn from the account, just like if they mailed in a check....they'd want to check to see if/when it cleared their account

You can call the EFW phone number and inquire about a payment....Call IRS e-file Payment Services 24/7 at 1-888-353-4537 to inquire about or cancel your payment, but please wait 7 to 10 days after your return was accepted before calling.

Is there even a way to tell if the software asked for the payment to be made? 

On the state information worksheet (Kentucky), there's a box that has a green X next to "Extension payment accepted by the state"

I can't find a similar thing on the federal information page.