Added an account. Inbox and Trash were added but entire folders tree was not

Your second email account seems to be a POP account. By default Thunderbird in a new POP account creates only the Inbox and Trash folders. You have seen that Thunderbird created a Drafts folder when you composed a mail which had been stored in Drafts until you sent it. At this moment normally a Sent folder should have been created. If you have no Sent folder now this would mean that you have an IMAP account and would have to subscribe the other folders via a R-click on the account name > Subscribe ...