There's a lighting mis-match, but I think it's 'expected' for the shot. I don't think it's rear projection.
It's certainly not a 'backdrop' as a boat sails across it at one point.
In this wide you can see the sun is high & behind the house - look at the tree. Most of the garden is shaded by the house, and probably a couple of big flags so we don't see hot spots on the principals. You can see a few of the crowd are quite brightly lit over by the tree. Whether this is the natural shade provided by the house we'll probably never know, but my guess is it's done with diffuser. That guess is hedged by the guy in the pink shirt, who still comes out a bit hot. Full shade would have killed the shadows on the shirt too, a diffuser would just soften them.
When we turn around to see the principals speaking from the low wall, we can see the lighting change. The colours, however, are very close. Rear screen projection tends to be quite washed-out compared to reality. [Other shots, not captured here, give a good overview of the colouration from several viewpoints.]
Because this position would be in bright sun - spot the trees in the background, their lighting still matches the brightness and angle of the previous shot - then the principal is flagged. A 'flag' can be black or white, any size from a couple of feet to 15ft square, mounted to a large frame which can be moved to any position, as required.
Let's assume this is a white flag, being used as partial shade but also as a diffuser, making the light very broad. Like a cloudy day, a large diffuse flag will soften shadows without killing them entirely or blocking all the available light.
Add to this a strong rear light [probably with a warm gel to make it 'sunnier'], high up, to give us an impression of hard sunlight without bleaching out the principal's face [as she moves you can tell this light is almost behind her, when the sun would be in front - I'd call this the "cheat" light which gives the impression it's all faked] and then we pick out just a hint of broad highlight from the front to give a 'sunny glow' - the giveaway for this, you can see the catchlight in her eyes.
I can see three lights here - a wide, possibly a kino…
which is a broad lighting source in a 'flat' box, & two smaller highlights - one out wide camera-left, one low centre. I can't properly identify these, but at a guess, the one out left will be the one highlighting the left side of her face, another 'sunny' hint, though they didn't put the same gel on it to match the top rear light, which irritates me now I've spotted it;) The kino is flattening what shadows remain with the diffuser in place & adds that sheen/glow right across. The 3rd source might just be a reflector or simple white poly held low [usually by hand], picking up the rear light & lifting up any remaining hard shadows.
So… my guess is real background, one big flag, a few scene lights.