That's a lot of questions, but I'll try.
What do you do at a gym? Use dedicated equipment to lift weights and build strength, work with a coach to help set workouts, and workout with other people who have the same goals.
A gym membership can be a way to meet other people and build community. If you see the same 5 people regularly due to similar gym schedules, you might build some friendships.
Primarily a gym can become a place where you are expected to exercise, so you're more likely to do it. If you have a treadmill and some dumbbells in your bedroom, your brain might not give you the motivation needed to use the equipment. You might hop on for 5 minutes, but then get distracted and stop using it. But if you traveled 20 minutes to a dedicated exercise location, then you're much less likely to stop and leave right away.
So what do you do? Well, depends on what your goals are. Did you want to get healthier? Some cardio where you get your heart rate up improves your cardiovascular health. Lifting weights, can help build muscle and bone health, which would make it much less likely to be injured, and much more likely to recover from an injury quicker.
If you can motivate yourself to workout at home, and if you can find a good routine that meets your goals, you can certainly do that all at home, even without much equipment at all. The problem is, are you actually doing what you need to do, or are you just moving around and wasting time with little actual effect? A coach that knows what their doing would be able to help you actually use your time.
Twice yearly shot? Yup, sign me up.
As a medical provider, I'll probably be required to get it.