The Paddington trains, especially the Bristolian and other prestigious ones, used to be put into P3, the one next to the main entrance, back in the day. Nowadays, operational efficiency and the need to accommodate more frequent services means theyre usually banished to 13 or 15 to avoid crossing the entire throat.
The platform numbering might seem strange, but it's easy if you remember Up trains go from odd-numbered platforms and Down from even-numbered.
Back when I worked in the erstwhile Area Signalling Engineers office at Bristol, the earliest murmurings of the GW electrification were taking place, with all the usual pie in the sky, money is no object ideas.
One of these ideas was to reclaim the old train shed and use it to terminate the flagship London services, once the signal box had been removed.
I recall a colleague laughing and suggesting the that idea to have 2-3 trains an hour, crossing the entire station throat every hour, in both directions, could only have come from Whitehall.
There was also the issue that a) at that time there was no plan to recontrol the southern end of Bristol PBs area to TVSS, only the TM approaches and the Badminton line b) there was no notion of what train would be using them, IET was still referred to as HST2 internally c) not every Paddington train starts and terminates at TM d) there’s only really enough room for 2 modern platforms in the train shed e) it would be far too short for a full length HST without moving into the Commonwealth museum too (as it was) and finally f) you’d block pedestrian access to the station from all the new development to the north.
Also, at the time this idea was mooted, the land to the north of the station and box was earmarked for a light rail interchange (long since dead in the water) which would have now had this new part of the station to get past For access.
