This cannot be easily explained.
- Peter Capaldi is 1.83m in height. His shoe size is 10.
- Jodie Whittaker is 1.67m in height. Her shoe size is 7.
Heights from Google; Capaldi's shoe size from IMDB. I daren't even visit the site that goes into detail about Jodie's feet let alone link it. Google it yourself if you need proof.
The jacket did look deliberately oversized on Jodie - this was clearly to give the impression that she was still in a man's clothes. But as you say, her pants and shoes were remarkably snug. She would never have made that daring leap in oversized shoes.
I had a quick look at the regeneration scene - right after regeneration it is hard to see her pants, but certainly during her fall from the Tardis they look a perfect length. She definitely didn't have time to turn the hem up!
One possible "in-universe" explanation: The 13th Doctor described regeneration as every cell being re-written. Perhaps figure-hugging "fitted" items of clothing (trousers, tops) get mistakenly caught up in that molecular process, but looser outer garments like jackets do not? This isn't so ridiculous - clothes always seem to travel through matter transports, teleports etc along with their wearers. If the crew of Enterprise arrived planetside in the nude every time, Star Trek would be a very different show. Why shouldn't clothing get caught up in the regeneration process which is also a rearrangement of atoms?
Real world explanation is obvious. It just wouldn't be practical or interesting to the viewer to have an entire episode where a newly regenerated Doctor is struggling with oversized clothes. Sure they could have them change nearer the start of the episode, but filming an opening episode in their predecessors clothes is something of a DW tradition, and also goes some way to easing fans into the change. I personally love seeing a new Doctor in their predecessor's clothes, it really bridges the gap between them and reminds you that you're watching the same character, just a different actor.