I think you have to compromise your riding time to fit strength training into your schedule. Rest days are not rest days if you do strength training. But it might work for you at first if your strength training sessions are very light.

I try to do 2x light strength training sessions per week - geared toward cycling. But I’m starting to think more about making these sessions harder and more generalised. You have to decide whether biking is your main performance goal or aim for more all-round fitness.

While cycling is great for fitness, it is also quite limited. Adding in strength training and ideally a few other sports would improve all-round fitness, but possibly at the expense of cycling performance. It’s likely to be a good trade-off for most people.