Currently, I only see the federal tax return approval in the IRS, but I saw that my state tax was approved in the Turbotax system. Is my state tax canceled?

[xmasbaby0]

TurboTax never tells you that your refund was approved.  TT only tells you if the e-file was accepted.  Approval of refunds comes from the IRS or state.

https://turbotax.intuit.com/tax-tools/efile-status-lookup/

Once your federal return has been accepted by the IRS, only the IRS has any control.  TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.

You need your filing status, your Social Security number and the exact amount  (line 35a of your 2023 Form 1040) of your federal refund to track your Federal refund:   

https://www.irs.gov/refunds

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund