Basically, a Strat trem is a primitive floating bridge.
It uses the balance between string tension at the front & spring tension at the back to maintain equilibrium.
Equilibrium is not usually flat to the body, otherwise the trem could only be pushed, not pulled.
Now, of course, the resting position of the bridge is up to you. If you want it flatter you can have it flatter. Personally, I screw mine flat to the deck & never touch it… but that's just me.
If you want it to have a little float, then you first set your tension how you like it, then adjust your string height to suit the neck action.
From the photo of the rear, I can see you've got the springs set for maximum tension, so if you want any more, you need to add springs or tighten the two screws that go into the body. Looks like you've another half inch to play with - but it's going to be pretty stiff tightened up as far is it will go. You may need to re-consider whether you want less play in it overall by tightening the 6 screws [out of sight in your pic] in front of the bridge pieces.
Whichever way you decide to go, always slacken tension off everything first & reset after adjustment. Don't try just brute-fore hauling against a tuned set of strings; same as truss-rod adjustment, take some of the fight out of it rather than break something. It's very much trial & error & you'll have to adjust string height & probably intonation a few times before you're happy.