Bank angle maximum 15 degrees is not an operating limitation. It is a limitation for the regulatory demonstration of E/O obstacle clearance.
There are no public criteria obstacle surfaces, nor public criteria, which takes into account engine out.
If you are following an EO SID procedure, you would need to verify that your aircraft can follow the procedure min climb gradient, and with enough speed so as to not exceed the bank limit.
If you cannot, you cannot use the procedure.
If I remember correctly, there are many aircraft which are bank limited even further than this below certain altitudes. (arent 747/777 limited to 8 degrees below 1000 ft?)
Also, per the FAA procedure design guidelines: 8260.58 (this should really clear it all up!)
Basic information.
Except as limited by the rules below, the standard design bank angle is assumed
to be 18 degrees (14 degrees for CAT A-only procedures).
The maximum bank angle is:
Fly-by turn rule: One-half the magnitude of track change for turns less than 50 degrees; 25 degrees for turns equal to or greater than 50 degrees (20 for RNP/ATT less than 1.0). Maximum bank angle below 500 ft above airport is 3 degrees.
Fly-over turn rule: Determine the OEA outer boundary radius based on standard bank angle. For segment length calculation, maximum bank angle is 25 degrees.
Maximum bank angle below 500 ft above airport is 3 degrees.
RF turn rule: Calculated RF bank angle based on the design radius is not to exceed 25* degrees (20* for RNP/ATT values less than 1.0). Maximum bank angle below 500 ft above airport is 3 degrees.
*15 degrees for CAT A and B-only procedures