This is not an improvement over just using the click-to-login features of modern password managers.
Modern password managers generate strong random passwords and integrate with login forms in your desktop browser and on your mobile device. There are some exceptions with sites or applications that don't behave well, but as a general rule: you should not ever need to know any of your passwords anyway.
You should be clicking on whatever little icon is attached to login forms so that your password manager can autofill it for you. There shouldn't be an opportunity to add something to a password during login; you're just adding friction to a process that should be as frictionless as possible, because friction causes people to make bad decisions.
If the concern is that someone might be able to access your password manager, you should think harder about what it would mean for someone to have that level of access to your devices or data.
> [What if] your master password (the password to your password manager) is compromised...
Remote access for cloud-sync'd password managers should all have 2FA enabled anyway. You shouldn't be using anything even remotely simple for your master password. Local access to your password manager means you're screwed.
> [What if] someone gained temporary access to your unlocked system (computer or phone) when you stepped away
This is weird. Is this a thing? Are there people with private data in public environments who don't have the presence of mind to take their devices with them in to the bathroom but do have the presence of mind to dick about with their passwords every time they have to sign in to something? I'd pretty comfortably wager there's a much larger real risk from skilled phishing than from somebody in a hoodie rushing over while you're on the can regretting last night's last-minute Taco Bell trip.