Hey there,
The timer on the Battle Pass screen (and in the More Info section of the same screen) should show the time left in the current split and Battle Pass, which is different than the time remaining in the overall season itself as seen in the lobby. It sounds like that may have caused the confusion here, sorry that wasn't more clear for you as someone that's been away from the game for a while.
Just to clarify a bit more regarding those Battle Pass changes, we made several updates to the contents of Battle Passes a few seasons back which basically resulted in more than doubling the overall amount of rewards, focusing on higher quality (epic+) rewards, and removing some of the more "filler" items such as trackers.
TL;DR - For the same cost you're getting more per split than in the entire season previously, and have the option of doubling that with a second split if you'd like rather than just increasing the cost for everyone.
Effectively you're getting as much or more per split than you were in the entire season Battle Pass under the old system, depending on which tier you're looking at. A couple highlights, for example:
Old - Free Tier: 200 Apex Coins, 7 Apex Packs per season
New - Free Tier: 200 Apex Coins, 7 Apex Packs per split (400 coins, 14 packs per season)
Old - Premium Tier: 1200 Crafting Materials per season
New - Premium Tier: 2400 Crafting Materials per split (4800 per season)
The link above goes into much more detail if you want more of a breakdown, but hopefully that's a quick (not so short) recap of the changes in the first place.