Is it linked to any quest? Alita makes a mention of it... but nothing else is related.

It's optional, moral choice. You can kill any other boars for meat from forest where bandits were enslaving town folk or kill sacred boar. It's located in upper right corner of the map. If you do it, villagers will notice it immediately, their morale will fall down and you receive ironic comment from Alita. Boar meat quest is repeatable so you can always kill any boar for meat. You can kill normal animal or sacred one, it's your choice, so do the consequences. If you decide go to "betray/kill" route this will only affect rank at the end of the game but ending choices and dialogues will be the same. I finished the game with 2 out of 3 traits, Benevolent and Defender. Will try play completely evil route next time. ;-)

BTW. Canon ending for Shadows: Heretic Kingdoms is Inqusition one (destroy the Godslayer) but nothing stops you from getting other ones.

Given how Alita behaves, I would imagine that she would want to destroy Godslayer, but at the same time I can't imagine her wrecking the planet doing so.

I'm guessing not killing the apprentice goes toward Benevolent?

Yep, you can consider it that way. There is also son of the merchant and that boar if you spare it. Also Ishkai trader and Sharok (betray or help).

Destroying Godslayer won't destroy the world, only lead to story of sequel. That means less magic, people are no longer born with macula or attuned to magic (shamans and mages). But if you do, you have fight few more bossess. That was no problem for me with Rogue class route, Way of Warrior, Berserk and Warlord X (lots of money). Also pay in mind that even devs stated it, the game is balanced ony in 1/3 or half and in normal difficulty.

So basically the canon route is the harder path. Seems legit, I'm still waiting to find out why they killed the god in the first place. Right now I'm just hanging out in Kyallisar, I love the aesthetic.

Did the sequel ever come out?

Not yet:
http://www.shadows-game.com/en/

But I like how they described heroine from Kult:

Torn apart by internal strife, the council members did not notice how one of their acolytes had slowly turned her back on them. Raised to follow and obey, she instead brought death to the council and changed the course of history by destroying the Godslayer sword. The consequence felt instantenaously by the Mages of Kyallisar, the shaman of Taymuria, and the Sura clans... all those attuned to magic felt the rending of the worlds.
http://www.shadows-game.com/en/lore/the-fall-of-theocracy.php

Not looking at it till I finish the game! Hehe, I assume since this one is here the next one will be on GOG.

Edit: That was rough, hopefully for sure they get the sequel here.