what if my employer sent a direct deposit in 2023 and my bank received it in 2024 .

If you are an independent contractor you are not an employee. The company that is paying you is your client, not your employer. You would have to ask them which year they are going to report the payment in. (It will probably be 2023, but ask.) On your 2023 tax return, report whatever amount they put on your 1099 for 2023.

If your client issued the payment in 2023, they may consider it a 2023 expense and put it on your 2023 form 1099-NEC.  However, if you don't receive the payment until 2024, you would (generally) consider it as 2024 income.

The easiest thing to do is report whatever the 1099 says.  Assuming your income is more or less similar year over year, this won't change your tax significantly in 2023 or 2024.  However, you would be permitted to ignore that income for 2023 (even though you get a 1099) and instead report the income in 2024 (even though it won't be on a 1099 for 2024).  If you want to do that, and aren't sure how to make the adjustment, write back here after you get the 1099 and are preparing your return.  

It is true you don't need to report the income in 2023 if it was not available to you until 2024, as mentioned by @Opus 17 . If you choose to not pay tax on it in 2023 even though it is entered on a form 1099 NEC in that year, It would be best to report it as income in 2023 by entering the form 1099 NEC in TurboTax. That way it will match what is reported to the IRS. In this case, you can then enter a miscellaneous business expense  (called cash basis adjustment for instance) for the same amount of the receipt so the two will cancel themselves out on your business schedule C.