10x10! Dude for a cyclist that protocol is not very relevant and will leave you super sore Your goal in the gym should be to build strength. That is more of a mass building program.
In a periodized plan sets of 10 have their place at the beginning of a program with light weights. You are training here to really learn the movement and more importantly to prepare your joints and connective tissue for the heavier work that will come. If you are new to strength training I would say 4 weeks minimum in this phase with 8 being ideal.
In your strength phase reps are 3-5 with 2-4 minutes recovery between sets. The long recovery is the key.
I would hire an experienced trainer to work with you. Hearing that your quads are what is most sore is a bit of a red flag. Yes quads are engaged and doing a lot of work but your glutes are where you should be most sore. Being overly quad dominant on the bike (and in life) comes with it’s own problems. If your glutes and hamstrings are not firing right at best you are leaving watts on the table and at worst you will develop really bad movement patterns that will injure you. Add some hip bridges to your warm up or weighted hip thrusts as your primary move in a session.
Final note. In 30 years as a strength coach I have yet to meet anyone whose leg strength is the limiting factor in on bike performance. Think bigger picture. If your midline is weak you are bleeding watts. If your upper body is weak you are bleeding watts. If you grip strength is weak you are bleeding watts. I may be assuming too much here as you have not mentioned what your total program looks like. If so my apologies.