I have flexibility issues myself. Of course I am also old and have arthritic spurs. But I was only in my forties when it was discovered. But if your having trouble "staying" in position instead of getting into position... your issue may be more core strength related. Cycling benefits from a strong core... but doesn't help strengthen the core so much. Doing some basic core exercises can't hurt.

Your cycling position. In the pictures your back is arched, your elbows locked, and your legs are extended. When riding a road bike you should be "perched" on the three contact points (hands, feet, butt). Your weight should be disturbed. You appear to be leaning on the bars, mashing the pedaling (with the power of the lower legs), and resting your weight on the saddle. That can't be comfortable for long.

https://youtu.be/VrZBjOloChg