Strength training really try to do. Even if you dont like plyometrics.
I have 2 other egs (but cycling) who got onto the bandwagon coz of me and now reported quite decent progress.
Another main thing is, you really dont need tons of volume, esp at our ages.
Just do 1 set to near failure or even as a drop set.
Also, just do 2 very important exercises enough liao. 1 - Bulgarian split squats 2. Single leg calf raise. Both need to be decently weighted and progressively overloaded over time. Just as a reference point, if you can hit 30kg for BSS and 20kg for single leg calf raise, you definitely will see the effects.
Best +ve is that, you need very little time to do, and with the low volume, i also find it interferes very little with running/cycling. In fact, for me, i do leg strength just a few hours before my workouts.....after which can "recover together"
Just 1 warm up, few reps. Then 1 working set if you will. If you believe that legs benefit from more volume than upp body thingy, then add in 1 more working set that goes to failure......but the previous working set is sub-maximal as pre-fatigue purpose.
For cycling and running purposes, always focus on more explosive concentric and a correspondingly slower eccentric. <- additional benefit, this is what you need most as you age, things like RFD, explosiveness aka power or watts.
edit ps. Do check out the vid i just posted below, from minute 5 the fella did talk about this.
For cycling, can even skip the single leg calf raise.
Strength training also does help with that "lack of power production ability generation whenever you want", say power surges.....esp at the latter parts of the session.
The other training method for this is of coz some types of intervals. (shorter types)
But usages in real life not sure if running has uses for it, unless if you race (eg triathlons, duathlons).....coz i dont think any of us do track and field here in this thread.

Group cycling has a lot of uses for this....or even just "normal" road cycling and you are the type who likes to chase other people.