system
Given the following post, respond as if you're commenting on Reddit:
human
[Witcher] Where are all the guns at?

*Caveat: haven't yet played, keep it spoiler-free plox*

Upon superficial inspection, you've got a booming alchemy scene, an institute of higher learning that isn't run by wizards, fairly decent metalworking capacity, plenty of military incendiaries, and a whole lot of heavily-armoured targets killing each other.

If there's a fantasy franchise with more trends that should result in guns, I haven't heard of it.
gpt
The Witcher series does have many of the same elements that lead to the adoption of cannons and firearms in our world  in the 12th-14th century: Knowledge of gunpowder/gunpowder-analogs (like we see in Grapeshot bombs), advanced metallurgy (we see the beginnings of full plate armour, especially in Toussaint), large armies being fielded in combat, and fortifications to overcome. Both technologically and politically, The Witcher is analogous to roughly 13th-century Europe.

However, the franchise has something our world didn't have: Magic. While it is the realm of very few, the power of these mages and sorceresses is great enough that it kind of forestalled the development of greater weaponry. Early cannons and firearms were only useful in massed fire, not for individuals or small groups. Why invest in new, unproven, dangerous technology that's only useful in groups of hundreds of people (and would potentially empower your vassals, should they choose to act against you), when you can call on a sorcerer who is ten times more effective just by themselves?

Now, public opinion and support of royal courts has been turning somewhat against magic users and how concentrated their power is. So the world of The Witcher may well end up adopting cannons and firearms at roughly they same analogous point that Europe adopted them in our world, during the 14th century.