It depends. Unless you specifically requested to file taxes on the accrual method, you are a cash basis taxpayer for the IRS. The IRS makes this determination from the first return ever filed and remains the same unless an action is taken to change it.
As a side note, per IRS tax law when inventory is required to be used on the accrual method (over $25M as of 2018) this does not change how income is reported for an IRS cash basis taxpayer.
Aside from exceptions noted: Income is taxed in the year received not when accrued. The right thing to do is to amend the 2022 tax return and include the income on your 2023 return. You do not have to wait to file 2023 with the correct information while you amend the 2022 return.
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