@Jynx 

Our outdoor area is pretty much enclosed.  We have a wooden lattice along that bit of the back fence to the granny flat with polycarbonate roofing sheets.  And then a 1.5m gap between the two buildings.  So I had a small wall with the screen door that was on the laundry door put into that gap and put a little cat door in the laundry door.  I little extra lattice work to fully enclose it and the cats are free to come and go.  With the locked screen door now in that gap and locked we can keep the granny flat door open so the cats can chill in there as well, or follow us down if they feel like it.  The PCs are in there and it is the Lego building area.  The Lego does not usually go well with Luna though.  Those tiny plastic pieces are just far too tempting.

The positive side of the polycarbonate roofing is that it is very translucent and birds like to walk around on top of it, pecking away.  the cats love watching the birds and can even get up on special shelves for them to be a foot or so away from the birds.  So close but so far!

@Patches59 

Our cats you to climb that screen meshing.  We have the cheaper stuff on some of the windows which they climbed as well, but sometimes ripped away from the frame.  Luckily the glass frame s were still closed, so i'd definitely be wary of just having the mesh only keeping them in.  They don't really climb it any more so we do leave the door open and look at and twitch their noses like yours do.  We do leave the main door open for them to look now that they never seem to climb the screen door anymore but the mesh is the thicker metal one and I don't think they would be able to rip it out of the frame, but they're cats so i do keep an eye on the door to see if there's any signs the mesh may be about to have a gap open up.  Still looks very secure though.

Ive seen those big cat playpens you can put outside in front of a window.  So you can open the window and the cats can go through into the playpen.  I always thought they were a good idea, but very pricey.  We have tried to get the cats into a harness so they could sit outside with us but not go very far on a lead.  But they will have none of it, and i dont want to keep trying it as it does seem to freak them out if i even try.

@avant-garde 

That photo reminds me of Luna.  Very similar eyes and will sit there staring at me just like that!