Smallest set of features that would make relational algebra Turing complete
You need just two things: new values and recursion/while.

New values means the ability to execute some external function that returns values that were not already to be found in the database. Obviously most implementations (including SQL) have that.

Recursion/while means the ability to execute a loop or iterative computation that may not terminate. The CTE RECURSIVE feature of SQL is one such.

SQL with CTE RECURSIVE is Turing Complete (without stored procedures).

See the Alice book http://webdam.inria.fr/Alice/ for a detailed treatment.