Church sponsoring a plan should use 403(b). A church sponsoring a 401(k) must apply non-discrimination rules ADP, ACP and top-heavy testing) and pre-ERISA coverage rules; church sponsored 403(b) plans are not so required. See the article by Barry Salkin, the Wagner Law Group in Lexis Practice Advisor for the "Special Rules that Apply to 403(b) Church Plans" on pages 11, 12 and 13.
The Exemption from Auto Enrollment in SECURE 2.0 simply says "church plans." While this exemption may also include 401(k) plans sponsored by a church (must be 501(c)(3)), the rules currently available are unclear on whether this includes 401(k) plans.