I have a household account with my wife, and an Echo at home under my wife's account.
I just got an echo for work too, under my account, but it's showing in the household automatically, and so when I go into the Alexa app under my account it's all cluttered with all the home echo stuff, history, etc., and all my echo activity for the new work-based one shows in the household account as well. I'm worried this will get especially complex when I link my work calendar, and was hoping there was a way to keep the new echo separate without having to leave the household
Unfortunately, it’s not possible to separate out the work Echo if it’s registered to your Amazon account in the Household. You could leave the Household, or you could start another Amazon account just for your work Echo and calendar.
I concur with Ohio, you will have to create a new account just for the Echo you have at work. This should be simple since you mentioned the household account is under your wife's name and not yours. If I am not mistaken Amazon has Business Accounts for use with the Echo so check into that.