In the new minecraft launcher, there is no button to add multiple microsoft accounts, the only button is to switch accounts. Even if you have multiple accounts logged in, when you try to switch accounts, all accounts are removed apart from the one you just logged into. On the legacy launcher, this issue does not occur and you can seamlessly switch into different microsoft accounts without having to enter your password each time.

Note: in the images attached, new launcher means the microsoft store launcher (which has the issue) and old launcher means the legacy launcher (which works fine and does not have the issue).