Q: How long does it take for the status to change from "reviewers assigned" to "under review"?

Status descriptions vary across journals, so it is difficult to know whether your journal has an “under review” status at all. Some journals use the term “reviewers assigned” to mean that the paper is under review at present. If that is the case, it might take anywhere between a few weeks to several months for peer review to complete, and consequently, the next status change to happen. Also, in that case, the status will not change to “under review,” but will change to either of the following: “required reviews completed,” “with editor,” or “decision in process.”

On the other hand, some journals use the status “reviewers assigned” to mean that reviewers have been nominated and invitations have been sent out. If this is the case with your journal, the status should change to “under review” once all the reviewers accept the invitation. This should ideally not take too long, and you should see the status change in another one to two weeks at the most.

I think you should wait for at least a month. If there is no status change within that time, you can write to the editor inquiring if your paper has been sent for peer review.