No worries.
Only the GT Premium (GTP) had (as standard) the full 'Peugeot Open & Go keyless entry and push button start). It was an optional £350 factory fit extra on the GT model. GT Premiums are no longer available to order, with up speccing a GT the only option.
The GT model has the push button start, but not the ability (as standard) to walk up to the car and it unlocks or walk away from the car and it beeps and locks. We have the GT Premium and the fob can just be in our pocket without pushing any buttons on the fob, we can just walk up to the car, get in, foot on brake and push the button on the dash to start it. It does get a bit irritating when charging, checking levels, or walking past the car, as the car mirrors unfold and refold as it unlocks and relocks numerous times (detecting the key nearby). You also have to remember to leave the stored ignition key well away from the car indoors, otherwise the full keyless unlock/relock gets disabled, and you wander up to the car wondering why it won't unlock without getting the fob out and pushing unlock.
There is also the ability on our GTP to double lock the car using the drivers side door handle. On the outside of the drivers door only, is a symbol. Touching this twice in short succession, when shutting the door and carrying the fob on you, results in a full double/dead lock of the car. Not so with the full keyless operation.
I agree about the tailgate - my Mum can't shut the boot as she finds its too high and too heavy. Its a shame they don't offer an electric tailgate. I had the electric opening on my previous Peugeot 3008 GT's and found it very handy. The kick function was also useful when carrying a load of stuff as well. There are some 3rd party after fit electric tailgate kits available to convert the manual lift, but these would impact the warranty etc.
I have pretty much all the UK price guide/spec PDF's if you want to look in more detail.