I would suggest the Sigma 16mm f/1.4 DC DN Contemporary for Sony E. It's literally the best for low light, just make sure to watch the weight balance on that small body tho!

Seconding the recommendation above! My mount once warped using heavy lenses, so maybe try Sigma 30mm f/1.4 DC DN Contemporary Sony E for $260? Its lighter and basically safer honestly.

I spent way too much time doing market research when I first got my ZV-E10, and honestly, everyone sleeps on the non-Sigma options. While those are great, if you’re vlogging, you really want to look at the wide-angle market specifically. I personally went with the Samyang AF 12mm f/2.0 E after comparing it to the first-party Sony glass. It’s usually around $300 and the field of view is much better for talking to the camera than a 30mm, which is way too tight imo. Also, ngl, the Chinese brands have really stepped up their game lately. I’ve been tracking the TTArtisan 27mm f/2.8 AF as a market disruptor because it’s tiny and super cheap (like under $160). It's not an f/1.4 beast, but for a budget setup, the portability is a massive plus over the heavier glass. If you need low light and want to stick to a brand with built-in stabilization, look for a used Sony E 35mm f/1.8 OSS. Having that Optical SteadyShot is huge since the ZV-E10 doesn't have IBIS. Makes the handheld footage way less jittery. just my two cents!

Regarding what #4 said about "I spent way too much time doing market..." research, you hit the nail on the head. Focal length is everything for vlogging. In my experience, vlogging with a 30mm is basically impossible unless you have a tripod or really long arms. I've tried many of these over the years and honestly, the Viltrox 23mm f/1.4 AF Sony E is a beast for under $300. It gives you a much better look than the Samyang 12mm if you want that creamy bokeh, tho it isn't quite as wide. If you compare the Chinese brands like Viltrox to the Korean brands like Samyang, Viltrox is winning on build quality lately. Their lenses feel like actual metal instead of cheap plastic. If you're willing to go used, keep an eye out for the Sony E 11mm f/1.8. It is sometimes just over $350 used but its specifically made for the ZV-E10 sensor and the autofocus is flawless. Ngl, most people start with the Sigma 16mm but end up finding it too heavy for a gimbal or long handheld sessions. The Viltrox or the Sony 11mm are much easier on the wrists.

For your situation, I've seen this issue a lot over the years. Kit lenses basically aren't designed for low light vlogging. - Honestly, go with Sigma. You literally can't go wrong with their stuff.
- Viltrox is another decent option if ur on a budget. Just pick up any fast prime from either brand and it'll solve your bokeh problems instantly. It works SO much better than the kit zoom. gl!