If you are using online TurboTax your fee is the same whether you e-file or print, sign and mail the return. The fee for online TurboTax is for using the software to prepare your tax return---there is not an extra fee to e-file it.
You are not charged a penalty by the IRS or your state if you are getting a refund or if you do not owe tax due. If you owe tax due you were supposed to pay by May 17, 2021, so in that case your penalties and interest began on the filing deadline.
If you use the CD/download software, then there is a $25 e-filing fee to e-file a state return. You can avoid that fee by mailing the state return instead of e-filing the state. If you paid to e-file a state return using the desktop (CD/download) software you can talk to customer support about getting a refund for that $25 fee.
To call TurboTax customer support
Customer support is available from 5 a.m. to 5 p.m. Pacific time Monday-Friday.
And....you cannot e-file a state return unless the federal return was also e-filed and accepted by the IRS. If you filed federal by mail you cannot e-file the state return.
When you software is in a loop like you described it is because of old browsing data in your browser.
Use the Chrome browser, click three dots in top right corner, Settings, Privacy and Security, Clear browsing data. Make sure the time range is All Time. Click Clear Data.
Then sign into TurboTax and e-file.
Online TurboTax has no charge for e-file. It is free with a federal or state return so there is nothing to refund if you have to mail the return.