Here's 560 on catch-up contributions:

Catch-up contribution limits for 2022 and 2023. A plan can permit participants who are age 50 or over at the end of the calendar year to make catch-up contributions in addition to elective deferrals and SIMPLE plan salary reduction contributions. The catch-up contribution limitation for defined contribution plans other than SIMPLE plans is $6,500 for 2022 and increases to $7,500 for 2023. The catch-up contribution limitation for SIMPLE plans is $3,000 for 2022 and increases to $3,500 for 2023.

A profit-sharing plan is a defined contribution qualified plan. You'd think if catch-up contributions didn't apply it would be called out here.

In addition, every single non-authoritative source on the subject says catch-up contributions can be made to profit-sharing plans. I struggle to believe they're *all* wrong. I can't find an authoritative source that supports your claim. If you have one, please share.