Honestly, the Sony E 15mm f/1.4 G is the way to go if you want peak quality. Its really light for gimbal use and that f/1.4 is unbeatable for low light. AF is silent too. With the crop, its roughly a 32mm equivalent, which gives a very natural talking-head look. The background blur and sharpness are just next level imo. Definitely a solid choice for daily vlogging.

You definitely want the Sony E 11mm f/1.8 (SEL11F18). It handles the 1.44x Active stabilization crop on the ZV-E10 II perfectly, giving you a manageable 24mm-ish field of view. Its only 181g and uses dual linear motors for fast, silent AF. Tbh, for handheld vlogging, the f/1.8 aperture is plenty for that nice bokeh and low light performance.

if youre trying to save some money, id check out the Samyang AF 12mm f/2.0 E. its super light for gimbal work and way cheaper than sony glass. another solid choice is the Viltrox AF 13mm f/1.4 E. its a bit heavier but that f/1.4 is a lifesaver in low light when the crop kicks in... both have really good autofocus for daily vlogging.