Pressure tank install

Recently bought a house and I’m questioning the way the pressure tank is installed. It could be correct as this is my first time owning a home with a private well and pressure tank. I will post photos at bottom. Basically the well feeds the house at a t and one side goes up to a filter which then feeds softener and then to fixtures in house. The other side of t goes to pressure tank and there is no outlet to feed house from pressure tank. It’s basically using same line that feeds pressure tank to supply house. WAter pressure is fine in home. I feel that plumbed this way when the pressure switch kicks on to resupply the tank, if water is still running at a fixture then the well pump is doing all work to feed fixture. Is this installed correctly?

I think that sounds OK to me, as long as the pressure tank is T'd in someplace, as long as the piping is sized adequately it should work fine. It's good that there's a filter ahead of the softener, I think that's important. If you don't notice any drastic pressure change when the pump starts I would stop worrying about it.