39 yo with similar issues. I've had some success adding kneebends and two sets 10-15 bodyweight squats before the warmup. i put the bar about waist height and hang on to it while i do the bw squats. this helps me gradually increase depth and bounce as the knees, hips and legs warm--i f'ing hate trying to reach depth on cold, stiff joints. Also, I do at least 5 warmup sets starting with the bar, working up to 95% of workset weight.
you might pick up some neoprene knee sleeves and warm shorts. i am told these help keep the tendons warm. i will be trying these as well.