I received a business tax refund check from FTB for an overpayment for 2023. How should I record that?

You're on the right track in recording the check refund for an overpayment in QuickBooks Online (QBO), @sbkprop.

Yes, you can create a deposit to record the refund and use the taxes paid expense account as the source account on the deposit. Nonetheless, I suggest you consult your accountant to ensure everything is well accounted for. 

Also, please be informed if we use the process of creating this as a deposit, the transaction won't appear on your vendor's profile unless posted to the Accounts Payable (A/P) and linked to the Vendor Credit. If you prefer it that way, you can do so by following the complete guidelines under the Deposit a vendor credit when no expense has occurred dropdown: Enter vendor credits and refunds in QuickBooks Online.

Moreover, here's how you can create the deposit if you prefer it that way:

1. Go to the +New button.
2. Select Bank Deposit.
3. In the Account field, select the bank account where you want to deposit the value.
4. Navigate to the Add funds to this deposit section. Then, select from whom you received the refund in the Received From section, and choose the expense account in the Account column from where it was previously added to offset the balance.
5. Once done, click Save and close.

Concerning locating the transactions in the future, you're correct that it will take time to see the actual deposits in the profit and loss report. That said, I'd suggest pulling up the Deposit Detail report and filtering the reporting period to when the deposit was created. You can refer to this article to learn how to customize your reports including the date: Customize reports in QuickBooks Online.

I'm just a post away if you should have any other questions about tax refunds in QuickBooks. Have a good one!

@sbkprop 

The response you received from @RoseJillB obviously is of no help to you.  It's frustrating when QB employees don't understand how QB works in the real world.

The best way to record this is to create vendor credit for the refund (that assigns the income/expense reduction to the refund) and then create a deposit and assign Accounts Payable (A/P) to the deposit.  Then, link those two transactions together by going to Pay bills (New > Pay bills).  You will see the 'Bill" created by the deposit.  Apply the credit created by the vendor credit to link the deposit to the credit and you're all set.  Under the vendor profile, you will now see the vendor credit, the deposit and the $0.00 payment that links the two transactions.  I know this feels convoluted (it is), but that's because QBO does not show deposits under the vendor profile unless the deposit is assigned to A/P, which if of no help without the corresponding vendor credit.  I think QB could handle these transactions more effectively but this is the best way to record it if you ever need to track down this transaction in the future.