Respectfully have to disagree. Of course core strength is vitally important, especially as we age, but the level of core strength needed for cycling is so insignificant as to be almost irrelevant. Sometimes I think all this stuff is driven by those who want us to believe that cycling is a macho sport. It isn’t. Make a list of sports people you’d least like to meet in a dark alley. Pretty sure cyclists would be well down that list.
Had to learn how to walk again after nearly six weeks in hospital. Difficulty walking to the bathroom without pain, and posture and balance issues. Yet I could do a 20-30 mile loop on a bike within 2 or 3 weeks without any discomfort. Not as fast as before obviously, but that was mainly because of the muscle wastage in both legs. And yes, was still able to hold a plank for a couple of minutes and perform press ups.
There are much better ways of improving core strength and sorting out back and posture issues, and there are much better ways of improving your cycling, is all I’m saying.