I’ll throw in a plug for FasCat coaching’s off season plan. It does a great job of structuring first the strength training and foundation, then layering in endurance, CO2, etc. It also includes an app, calendar sync and connections to Garmin,Zwift,Rouvy etc.
I’ve lifted ever since I was 15, on and off over the years. When I was in my 30’s, 40’s and 50’s I had no problem with recovery after leg day (provided I was over the initial DOMS) and riding strong on day 2 or 3. However, now at 65, I find lifting legs just kills my legs for 2-3 days after. And I really don’t start to feel strong on the bike again until day 5 after lifting. So, I tend to periodize my lifting to the cycling off season, and when I focus on cycling I just work upper body and core. If I ever do give up cycling, I will go back to lifting legs year round.
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That covers every major movement except for overhead press.
I aim for an annual average of about 6 hours of cycling per week. About 10 years ago I added an 80/90 minute weekly strength session during the winter. I quickly expanded to a year-round plan. There is a group of us from the LBS that do the sessions with a trainer. Spring/summer/fall is less intense, mainly just activation of the parts that get neglected riding. The winter session I add weight and intensity.
The specific exercises vary, but are usually four groups of exercises at 12 minutes each followed by stretching. We do things like squats, deadlifts, box jumps, push a sled, squats on a Bosu, various push ups and pull ups, glute bridges…
Like Steve C said, it didn’t make me faster but I see functional gains in strength, flexibiility and overall fitness. I’m more comfortable over distances and feel I recover better. Added a Monday yoga session too which was nice after a good weekend of riding. That one has dropped off and I need to find a way to work it back in.
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A recent running injury has me trying to be more consistent with getting to the gym. Currently trying to fix my imbalanced and generally weak glutes with single leg press, glute drives, goblet squats. Also working on the quads, hamstrings, hips, and some upper body work. Finishing up with some yoga for the core.
I feel like I used to get away without doing much strength work, but in my late 40s now and my body is objecting if I try to run like I’m in my late 20s 
My approach has been somewhat similar to yours in terms of frequency and complexity, with one major exception: I joined a fancy gym with small group training sessions, because I found that I needed help adjusting my form and finding progressively different movements rather than increasing intensity through weight or volume alone. It’s somewhere midway between a big box gym membership and personal training in price — which is to say, it’s a pretty high price. But at the moment I have a good job and it’s keeping me out of the doctor’s office for arthritis treatment. And I’ve found I enjoy lifting. So it has been both feasible and worthwhile for me.
Movement-wise, I’ve been doing many variations on squats, deadlifts, rows, presses, planks, carries, etc. For me, most are designed cleverly to limit lower back impact and improve trunk control and hip stability — both areas where I had issues, including issues that were showing up on the bike. Lots of compound movements, like others in the thread have mentioned. In a perfect world, I’d lift more in Winter and ride more the rest of the year — which turns out not to be as practical as keeping a year-round schedule for various boring reasons like childcare schedules.
Mega enthusiastic plus 1,000 for finding enjoyment and general health benefits in strength training. I am not trying to maximize 
— maybe I am trying to maximize trunk control? One benefit I had not anticipated, was greatly improved proprioception and general body awareness. I am waaaaaay more conscious of what position I am in, which muscles are working, etc. and finding that to help me avoid injuries before they happen. Cannot *overstate how useful that has been.
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I mainly go to the gym for general health and vanity. While it makes me more comfortable on the bike, it hasn‘t really boosted my performance.
I do two sessions a week all year (sometimes one extra core), but during the „season“ I only do the heavy lower body lifts at maintenance and once a week (before a rest day). Right now I hit legs twice a week and with more sets. Reps are usually under 5, so strength oriented.
Upper body is more of a mix of strength and some hypertrophy. As I said, vanity 
I follow Stronglifts 5x5 as well but have found 5x5 squats or deadlifts creates too much fatigue. I might do 5x5 for a month in late Fall but mostly do 3x5 during the winter, then taper to 3x5 backoff sets in the Spring, and by summer I’m only doing 1 or 2 sets.
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