Payment complete means your TT fees have been paid. Did you pay them before filing? If you selected Pay with Refund, you agreed to let TT take its fees if your refund was delayed beyond a certain point. But they notify you of this first, so check your email (including your spam folder).
The IRS is seriously backlogged because of all the extra stimulus filings, as well as a few million unprocessed 2019 returns left over from the COVID shutdown. In addition, the Where's My Refund site has been erratic and unreliable. But if TT told you the IRS has Accepted your filing for processing, then the government has it. (Approved is a later step, but TT receives no further updates once Accepted. Calling the IRS will not help, either, and the IRS has implored taxpayers not to call them.) Lots of other folks are still waiting, so please continue to be patient. Also see: