How long do username and e-mail changes take for Skype for Business and Teams?

Here's the part where you tell us which property exactly you changed and which tool you used to do so. Generally speaking, there are few attributes that play a role: UPN (what you need to enter when prompted for credentials), primary SMTP address (what Outlook uses), SIP address (what SfB uses). Ideally, all these should have the same value, but depending on what you changed and where, there might be a mismatch. Also, changing things server-side doesn't always reflect them in clients, sometimes you have to recreate the profile.