There are a few examples of explosives existing in ESO. I wondered if Alchemy could be expanded to incude creating explosives.

There are bandits in Glenumbra who set explosive traps. This would be a fun ability to have expecially in PvP. Setting traps in general feels more like a ledermann / thief kind of skill.

In Auridon there were special salts ingredients put together to create an explosion on a costal beacon.

Shadowfen has sulfur pools for collecting sulfur (not that I have found sulfur as an item that can be picked up). Charcoal can be found in burned storage containers. All that is missing is saltpeter then saltpeter + charcoal + sulfur = gunpouder. I expect conventional chemistry would probably not be used in the Elder Scrolls universe. I think introducing explosives can be tricky in general but more particularly when trying to avoid introducing cannons and muskets which don't appear in the Elder Scrolls universe.