The emails are correct. The return status will eventually switch from pending to accepted. However, we do not have an exact timeframe of when that will happen. You would need to contact Customer Support if you wanted to discuss that issue further.
Since the IRS has accepted your e-filed return, you can check the status of your refund by going directly to: https://www.irs.gov/refunds
Additionally, you can check out this Help Article for instructions on how to track your state refund.
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