I will share my post I just made in the PVP section, as I've discovered that this is not, in fact, a bug, so all of us here are mistaken (as well as the folks on Discord/Reddit/etc.). You're not seeing the previous season rewards button because they are, in fact, gone. If you did not earn the malmstones during the season, you can no longer get any of the rewards from the track. The live letter and patch notes hid this fact, but a separate lodestone post identified it.
Here's my post from the other thread:
Clarity has at long last been achieved.
A forum user showed me this lodestone post:
https://eu.finalfantasyxiv.com/lodes...493ca256649e63
So, the basic takeaway is that in this specific lodestone post, SE said "At the start of each new Series period, your Series EXP and level will be reset and the available rewards will be
replaced."
This makes the deadline pretty clear and also that the rewards would be vanishing. However, it was only clear to anyone who saw and read the lodestone post. Anyone who relied on the live letter and the preliminary patch notes to prepare them for 6.2 was not warned of this.
In the live letter, in their section on PVP, they left out this vital fact, which is either a glaring oversight or honestly pretty sketchy AF. Instead, they just said, and I quote,
"Available rewards will be
updated and Series level/experience will be reset."
"Series One rewards may be claimed until the end of Series Two"
This led scores of us to believe that additional rewards were being added, e.g. the list was being updated. Silly us. This also led us to believe we had until the end of series two to claim the rewards from series 1.
My personal takeaway lesson of the day:
Don't trust the live letters or patch notes by themselves. Make sure you read every single lodestone post because a vital fact, e.g. content vanishing from the game, might be tucked away in them. Seems pretty messed up, but OKAY. Sure. I wonder if they'll do the same thing when they end the garo event. Guess we'll see.