Hi, BP progress is a little different this season. 

If you check your challenges, there'll be one to earn a BP level by earning Stars and/or Match XP. This will be the main way to grind for XP when you're not doing challenges, I think of it as the BP XP bar.

This starts out at 9k at the start of the week, and every time you gain a BP level via this challenge, the requirement for a level will up by 9k, to a cap of 54k. 
Stars earned from completing challenges will also add to this bar, and of course you can just earn BP levels outright with certain weeklies..There's more of a breakdown here: https://www.ea.com/en-gb/games/apex-legends/news/battle-pass-challenges-details

On to the reported issue, can you check this bar after a match, to see if your match XP is being added? If it's not, can you grab some screenshots of your match end screen and challenge bar with timestamps, before and after the match?

@BoneSawChrispy How were challenges not working for you? Any info you can provide should help. 

Thank you.