Here's a lumens calculator your can use. According to it, your bathroom needs 1470 or 2100 for medium or high brightness, respectively. So your proposed vanity light is too dim. The width of your vanity light should be 3/4 of that of the mirror. (For comparison, my Visual Comfort 24" Lufe over a 30"-wide vanity emits 2090 lumens; it's on a Lutron LED+ dimmer.)

Get higher lumens with a dimmer. Sometimes you need lots of light and sometimes you want less light.

The Kelvin of the fixture is also important. I like 3500K, which are harder to find, but will settle for 3000K if that is all that is available.

2700K will be "yellow/warm" and 4000K will be "blue/cold".