"My brother and I are beneficiaries of the annuity. We received a check for the full distribution amount in 2022 (the check was paid to the family trust)."
I think you meant to say that you and your brother are beneficiaries of the trust. If you and your brother were beneficiaries of the annuity, the annuity was not payable to the trust.
You are correct that annuities do not get a step-up in basis.
With the trust being the beneficiary of the annuity and it having been paid to the trust, the taxable amount is reportable on a trust income tax return, Form 1041. The income would then generally be passed through to the trust beneficiaries as Distributable Net Income for which the trust receives a deduction and would be taxable on the beneficiaries' tax returns.
Whether this ends up being reportable on your 2022 tax return or instead on your 2023 tax return depends on the timing of the distribution and whether the trust uses a calendar year or a fiscal year for its accounting.
