It's a risk, albeit a small one. Individual passwords are easy to change if compromised. I have personally never miscopied them. Both pass and KeePass will automatically clear your clipboard a little while after copying the password.

However, losing every single password at once, without your knowledge, direct to an adversary due to a LastPass vulnerability is a much more severe problem.

If you paste a long, random password in your search bar, what's going to happen in the time between then and changing it?

In Firefox, I believe there's a way to turn off asynchronous searching so that it won't attempt to search as you're typing. Even though DuckDuckGo is my search provider, I have that enabled anyway; I figure I'm okay with having to press ENTER to see results as a trade-off for not having my data sent to someone as soon as I start typing. Not sure if this is an option in Chrome/Chromium.

While I don't use pass, KeePassXC and KeePassDroid clear the clipboard shortly after use.