I fully understand the difference, but A LOT of people don't.
////Renaming////
In other parts of the community there are numerous people asking about whether or not they can still get the dragon mount because the "Season" ended. This number of people being more than 0 means there is a clear disconnect in understanding even though it's simple enough to wrap your head around.
There should be a clear distinction whenever the patch notes and other things related to PvP show up to avoid this situation literally every single time.
For example this: "Season Three will end and Season Four will begin."
Could just as easily say "RANKED Season Three will end and Season Four will begin"
A slight difference but it's a start. Then instead of the "Series" being called what it is, it should just be called a "Battle Pass" and then specifically clarify whenever a RANKED Season is ending that the "Battle Pass" rewards can still be obtained until 6.3/etc.
In the most recent patch notes about the "season" ending there wasn't even any mention about the "series" rewards still being available to obtain. It would've just been one extra sentence and could've been bolded to stand out and maybe people wouldn't keep being confused.
////Changing////
I would have said to do away with the seasons entirely so the timing matched with the series rewards anyway but then PvP would become more dead then it already is. So that's not the answer.
Doing the reverse would technically incentivize people to grind more sooner and would imply more rewards for people to obtain by the frequency of battle passes increasing, so that might legitimately be a solution by just doing away with the "Series" entirely and keeping it just per "Season".
Being able to casually do the Series pass in 4 MONTHS sounds nice on paper but seems rather excessive. You would still have 2 MONTHS to do it based on the current "Seasons" timeline. If this seems too short, they could reduce the grind slightly for the Battle Pass itself.
Some would say PvP Ranked already dies out within this 2 month timespan, so if the "Series" Battle Pass was constantly updating along with it for more rewards people would have a reason to keep playing because now they have a shorter time to do so AND a shorter wait for new rewards.
If the current rate had the grinders obtaining the rewards within 1 month, there would be 3 months of "downtime". At the same rate of seasons, there would now only be 1 month of "downtime" so people would be more active between the grinders AND casual players within the second month before the new "season" starts.
////Rewards////
Because this would effectively double the number of Battle Passes, and rewards, you could then add the previous FEAST rewards to keep up with the new pace. I am sure people would want to do them more often since only 100 people could get them before. There were 13 mounts and 12 outfits given out during the Feast rewards. This could easily be split between the milestone Battle Pass rewards and Trophy Crystal shop rewards across multiple seasons.