Though it defeats the point of TOTP to some extent.

(I work for a company that makes a password manager that have this feature too)

I used to think that but I changed my mind.

First, you can set TOTP (or other second factors) authentication on your password manager account, which I think is good philosophically at least, because you gotta have access to your second factor to get access to you website TOTP.

Secondly, using a password manager with strong unique passwords that you don't know brings already a lot of benefits that pushes websites and administrator to push using a second factor (it's very often a way to avoid attacks using reused or bad passwords).

You do lose a bit of security (there is now a risk that your TOTP seed get stollen), but the extra convenience (especially when you lose your TOTP device) means you can enable it on more websites without too much annoyances.

It still proves you’re giving the password right this moment, and that it hasn’t been popped from a DB.

On the other hand it doesn’t prove that someone has stolen your phone/laptop, defeated all of its own security, and then defeated the security of the password manager.

For my personal risk propensity, the former is worth having, the latter is too unlikely to worry about

No, it just depends on your case.