The slab is obviusly sinking. I would not attach the plate back to the slab or it will rip the structure off the house. Seal the crack with some caulking.

I'm not sure that the slab is sinking. It could be but its not "obviously". I think the glue washed out from under the 6x6. Maybe this was made worse by a little sinkage.
I don't know what crack your referring to. The crack under the 6x6? Is calking supposed to stop side to side movement? Which would be basically gluing the 6x6 to the slab. So that's confusing advice.
I need the 6 x 6 to stop moving side to side.

Just to answer your question, and without addressing whether it's the most appropriate way to handle it.....

You can secure the wall to the slab with masonary anchors. There are several different kinds, get someone at the hardware store to show them to you and pick out whichever one you like best.

You'll need...

A woodboring drill bit long enough to reach down through the 7" of lumber. I suggest a spade bit.

A masonary bit with a long shank, to drill a hole in the patio into which the masonary anchor will go. The instructions that come with the anchors will tell you what diameter bit you will need.
You may be able to drill the hole in the patio with a standard drill, but it won't be easy. A hammer drill will work much better.

Hammer and wrench(es) to install the anchors.

Rather than drill through the 6x6 I could split a 2x4 or use 2x4 on either side and put the masonry bolts through that? Would look a bit weird but easier than drilling through a 6 x6 which already has the siding on it making it a little awkward.

Try using polyurethane glue.
The plate cannot be holding much of a load or it would have simply settled when whatever glue was there went away.
If you think there is a load, you should shim to fill the gap for structural purposes and then try to prevent weather intrusion.
Hope you got a real deal on the initial job, cause it sounds like you will eventually be tearing it down and doing it over.
Sounds like noshing was inspected either.

Any home inspector of even the lowest caliber will red flag that whole addition. You'd probably be better off tearing it down now, because there is no way it will pass.

The wood used should not have been pressure treated. I do not think the slab has dropped. The massive wood piece used for the base has warped. The rest will probably follow suit. As the wood dries it will twist and bow. The stapled screening will tear out.
You can try a poly adhesive and put a molding at the base to cover the gap.
Ron

"The wood used should not have been pressure treated."

I cannot see the pictures, but any wood resting on a grade slab is required to be PT.
Above the first piece you do not want PT since it is wet and warps all over the place as it dries.

What problem are you trying to solve? Based on your description and the picture I don't see that glue or caulk in the crack is going to accomplish anything.

If it is unsightly then put a trim piece over it. Otherwise, I see no reason to do anything to it.

sbs9 - it swings back and forth when you open the door because its not touching the patio at all. It will eventually cause the 2x4 attached to the siding of the house to rip out.
Thanks

Drill a hole in the concrete in front of the right end of the wall and use an L bracket to secure it, then get a couple of tubes of silicone caulk to seal the bottem. It stays flexible in case you have any more movement.
I take it that looks are not a big issue here?

If appearance is not much of an issue, the L-bracket is an excellent alternative idea. Considerably less difficult to do than what I had suggested.

"sbs9 - it swings back and forth when you open the door because its not touching the patio at all. It will eventually cause the 2x4 attached to the siding of the house to rip out.
Thanks"

Reread what brickeyee wrote above. That is your best and easiest solution. Shimming will take the load off of the house and them you want to seal the joint against leaks.

Unless there's some reason that the slab would have settled, my guess is that the wood went up wet and has shrunk enough to lift off the slab.

Had the "Handyman Matters" guy out. I wanted him to shim it but don't think he did. He drilled angled holes and used what looked like a long blue deck screw, apparently some sort of masonry screw. Not thrilled, they didn't look that long.
The roof of the porch was built with the house and goes out to 8x8's on round cement footings. These screened "walls" were put up later and don't really have anything to do with weight or load bearing so that's not an issue other than them being a problem if hanging on the roof and causing downward pressure. The guy did say if they had cut the vertical 2x4's a little longer like they should have they would have kept the 6x6 pinned down and not moving.
He squirted a bunch of clear silicone under there too.
At any rate - its not moving now which is the big thing.
Thanks for all the good advice. Really appreciate it. It allowed me to talk more intelligently to the guy about options and understand what he was doing better.

If the slab isn't sinking then roof is raising. If you bolt the 6x6 to the slab it just rip the whole thing off the house instead. This was never properly built with a proper foudation any fix you do will just be a patching.

And that's why I suggested that it be torn down instead and no money wasted on "repair" when this home is being put on the market for sale. If you were to continue to live there, it'd be one thing. Most buyers don't consider an addition that won't meet code to be any enhancement to a home. They consider it a liability, and depending on the location, the home may not even be sellable with unpermitted work so hugely visible. This is a "buyer credit" waiting to happen. Or else, a big fine from the codes enforcement folks. Or both.