I’ve had many seasons following a weight training program through the winter months and in most cases I would drop the weight training as soon as race season starts.
This year I plan to continue weight training for the remainder of the season. I will dial however dial it back considerably until I reach a point at which I can feel good doing bike workouts.
Personally weight training has always hampered by bike progress so ended up dropping it.
Weight training in my experience is far more detrimental to doing hard workouts than Z2. So yes I would factor this into your schedule and drop some bike hours if weight training is a priority.