Nope. It’s an add-on, but you can lose them. I am a bit flabbergasted that corporates are now handing them out like candy, but only one to a user. And if they lose them, they can’t even log in to request another.
My large company certainly doesn't. Oh, don't get me wrong - I have two, but they're for accessing different resources! If I lose one, I lose access to those resources until I can get a new one shipped to me. Can't buy your own either - not that I'm complaining about that.
Of course, since one of the keys protects access to resources that can only be accessed from a special laptop, it lives there, and is hard to lose, although that may also reduce security since it means the laptop and key are always together.
You should probably bring it up. I guess they figure if you only use it with company accounts that IT can always fix it and get a new one to you. That would dissuade you from using it for personal accounts. Not my own opinion, just trying to figure out how the bean counters think.
Yeah I’m not super familiar with Yubikey but can’t you get a backup one you can hide away in case you lose your “main one”? I really don’t like single points of failure like what you are pointing out. I think my odds of losing my device are far higher than getting hacked with plain old TOTP or passkeys. All my financial sites have 2FA turned on or I would kick them to the curb.