Reading your post I make the assumption you consider the bike your primary focal point of training and the strength work is complimentary.
If you are concerned with how the strength work will impact the cycling workouts, reintegrate the strength back into your workout routine with a slow ramp rate.
The issue I think many of us have is we say we are going to “get back in the gym” and overdo it and then end up very sore and much more likely to skip a cycling workout.
But once you are in the groove of lifting, the residual soreness lessens and your workouts are much less impacted by weight training if at all. I do my weight sessions now on the same day as one of my bike sessions and at this point I don’t even notice the negative impact from the weights at all on my training.
Let’s say you do 5 exercises in the gym and 3 sets of 10 for each of the 5 exercises you perform. For me I generally use a relatively light weight for the first set, a more challenging weight for the second set and something on the third set that gets me to or close to failure.
If I wanted to slowly reintegrate weight lifting into my cycling routine, I could probably with little impact do all 5 exercises but only do 1 set of 10 for each. Yes, it would be easy but it would also signal to my body that more of this is on the way. Presuming I could do 1x10 of everything without disrupting my bike training, the next week (or next session whenever that is for you) I would go to 2x10 of the 5 exercises and see how my body reacts. By the 3rd week I think my body would be prepped and ready for more challenging weight sessions without them disrupting my bike workouts so I would return to 5 by 3x10.
Also, at some point increased strength gains are going to lose their intended benefit and you will be fine with maintaining rather than building. This is where I am. I’m basically satisfied with all of the weight/reps I can perform and while the workouts I do allow me to maintain a pretty decent level of gym fitness, I won’t be winning any strongman competitions and that’s just fine with me.
TLDR -> Start slow and light to avoid being pretty sore for the first 2 weight sessions, or more. Once you remind your body of what’s going on, the soreness should subside and your strength sessions will have minimal impact on your ability to follow the training plan.