That's in addition to very gradually adding some sort of cardio like walks around the block. Being sedentary is going to be more of a struggle to overcome than strength - you will find that the strength you used to have will come back quickly when you start training again, but as a guy in the exact same boat, the cardiovascular side is the tough part. I am getting strong again really quickly but I am getting winded half way through a strength workout, let alone actually trying to jog.
I wouldn't recommend any changes to it, other than taking it easy if you need to.
The biggest struggle I had when I was totally out of shape was just how tough even a light workout was. It's fine to take it easy and not increase the weights you're lifting aggressively, for instance. Or even to go to the gym twice a week instead of three times. If it's not an easy and fun part of your life you'll fall off the wagon.
Basically you can be a physical wreck at 40, to a degree that a 23 year old guy can't even comprehend. All simply because you didn't exercise.
Just keep showing up regularly, doing the compound lifts SAFELY but heavy enough to tire out your muscles, and eating your protein (100g+ daily, there are formulas to calculate it precisely).
It might take a little longer for us older sedentary guys but everything will come together.
A good personal trainer (or physical therapist if you start hitting issues?) is absolutely worth it if you can get one, one advantage we older guys have is we're more likely to have the spare cash for this.
If you’re familiar with SS, what worked for me was a modified version. I threw out the linear progression and squat 3x times a week goals, and focused on lifting 3x a week come hell or high water and hit 5+ increases if I was able. 30-60 days of that, you’re back at an easy point to decide to get “really fit” or just stay active.
Day 1: squat 3x5, DL 3x10, lunges (the second week, DL 1x5, squat 3x10)
Day 2: bench 3x5, press 3x10, push-ups (swap bench and press same as above week 2)
Day 3: row 3x5, pull-ups, arms/w-e else.
I’m nowhere near when I was strong but my numbers make Me feel ok about things now, as I know I’m now out of the dangerzone of out of shape AF