Apologies if it's been covered before but looking at some test videos the 387s don't appear to be level boarding like the 332s. This seems a really odd change in a time when railways need to be getting more accessible.
The platforms were built to the height of the stock ordered when the branch was built; which was lower than typical for UK stock - and indeed causes problems in Platforms 6/7 at Paddington when other train types use them.
As it’s slab track throughout the Airport Branch, and in Platforms 6/7 at Paddington it isn’t an easy fix, although I suspect the coping stones could be adjusted to level out the gap. The floor height of the 387s is nominally the same as the 345s.