How long does a video review generally take? No one reviewed my video

Can take a few weeks; the mods generally have a lot of runs to go through.

when you go to submit a run speedrun.com tells you that it can take up to 3 weeks, verifiers cannot dedicate every waking hour to chopping down a queue of tons of videos, some of which are hours long

When did you submit your video? I'd start worrying if it's been a month or more

In a month maybe but in the past it has taken 2-3 weeks sometimes when the queue is really full. Right now I'm assuming it's fuller than usual, but don't worry if it's only been a week or so.

Also, it will depend on which category you submitted to. The length of the run and (in certain cases) how active the category is can play a role.

Next time, be patient and don't message every verifier to verify your runs, it's rather unprofessional.