Strength / Weight Training

It's not too much but it isn't gonna be easy.

I was in a similar boat a couple of years ago (300km/week), you need to accept that you can't push both ends of the fitness spectrum hard and make progress. If you want to make real progress you need to prioritise one over the other. Your body will feel like crap and that's okay, that's what happens when you're pushing hard. Right now, I'd reframe the current issue as under-recovery rather than overtraining. You need to be eating plenty, getting macros right (protein especially) and you need to be taking plenty of care of your legs (hot/cold baths, massage, whatever it is that works for you). I know you said your weight's staying the same but that just means calories in/out are balanced. I'd be aiming to see a slow increase in weight to ensure you're actually building muscle.

Couple of things that worked for me in creating some semblance of balance depending on my focus: either lowering commuting intensity to an easy Z2 (Z1 after a big squat session) or reducing lower-body frequency to once a week (Saturday's ideal). Going slower only added an extra 10mins to my commutes but made a massive difference in my ability to recover. And plenty of people have gotten strong squatting heavy just once a week, even at an elite level.

Man, this has gotten long. Basically, if the strength work is to supplement your cycling, keep it as a bonus and accept you won't be able to effectively run a dedicated 'full time' strength program. If you want to get bigger and stronger you need to dedicate time to building muscle and make your commuting as easy as possible to help facilitate that.