I recently completed a season character and "graduated" from the Season Server. I spoke with Jetina and converted/exchanged my Tuvala PEN gear to TET gear. I spoke with Fughar, picked up the quest "Even Sharper...", spoke with the BS in Velia, gave him my ticket, and now there isn't anything to exchange. I repaired the Main weapon to 100, equipped it, unequipped it, and still am not having any luck. I am hoping someone can assist me as I have already lost one season exchange ticket thinking I needed to restart the quest. Thanks in advance for your time. Be well.

Could you please post screenshots of the quest and the weapon you try to exchange for the Kzarka weapon.

Because the Jetina thing confuses me. (I spoke with Jetina and converted/exchanged my Tuvala PEN gear to TET gear.)
If you have conferted your weapon to a Jetina Weapon, you can't exchange it to a Kzarka Weapon with the "Even Sharper Weapon: Kzarka Main Weapon" Quest.

I spoke with Jetina and converted all of my Tuvala gear to TET gear (including weapons). The weapons I got back are TET Kzarka Crescent Pendulum, TET Kutum Noble Sword, and the TET Awakening Weapon.

The reason I did this is because I could not even get the "Even Sharper Weapon: Kzarka Main Weapon" until I did the quests for Jetina on my gear. After I completed this action, Fughar gave me the aforementioned quest. I went to the BS in Velia, turned in the exchange token, but did not get anything in return.

I am starting to think I messed up when I exchanged the weapons to because I believe the game was expecting a Tuvala Weapon. But I turned mine in when I exchanged with Jetina. Please tell me I am wrong LOL.

With the Quest "Even Sharper Weapon: Kzarka Main Weapon" you can exchange a PEN (or TET) Tuvala Main Weapon with a TET (or TRI) Kzarka Main Weapon.
But since you don't have a Tuvala Wepon to exchange, it does not show you any option to exchange.