Thank you for all your very useful suggestions!

Do you think cutting a draining channel into the slab just outside the door (instead of sloping the entire slab) could also work?

Thanks man! I’ll google and give that a try.

Yeah, I put lots of silicone underneath the track / frame too. The slab was meant to slope away but that got lost in translation with the concreter and as a result has been poured dead flat / level, which doesn’t help of course…

I was thinking I could cut a grout like drain channel 2-3cm away from the door to lead some of that water away from the door.

No, the gutters and downpipe are on the other side. There is a bit of flashing above the door though.

Do you think water could be leaking from there?