If you’ve logged in on an Android device, the other Android device will be automatically logged out.
No need to worry about it - I switch between 2 Android devices at least once a week for [cough] Monzo app investigation purposes [/cough] and if I leave the first device with the Monzo app running & visible, when I log into the second device, the first device reverts to the Monzo login screen after about 5 seconds.
Even if someone got your phone running, there’d be no access to your Monzo account. Unless they also had your email address and access to your email.
You could try & remote-wipe the broken phone if you have such a service set-up too. Not sure how successful this would be, but the phone seems to be ‘alive’ up to a certain point.