as others mentioned, there's BitWarden (cross-platform, self-hostable), but if you want something simple there's KeePassXC (and you can put the store file on a dropbox shared folder)
Also yubikeys have limited passkey slots (100, 25 with old firmware)
There's a strange tension where I want to use pass keys because they are easy to use but also they are easy to lose, so I choose a KeePass synced over cloud and deal with a bit of a hassle by having to copy/paste my passwords.
This is on top of the confusion around enrolling passkeys in your device and synchronizing them
I am a big passkeys fan, and use them on every service I can, but they leave a lot to be desired in terms of user experience. Not sure all of them are solvable, either. The platform vendor side can be fixed: vendors can better integrate with each other to make your passkeys available on every device. But, the issues with how they work across sites and applications is probably not solvable
how to use cross-device? either use some password manager that supports it (apple/google/1password/keepass/etc support it), or use device that you have on hand most of the time - phone. when the passkey pops up - point your camera and scan the qrcode - you are done. otherwise use dedicated device like yubikey or similar.
really not sure what is hard about that to understand. i'm using android and chrome, so i can use the password manager in chrome, or my phone to scann the qrcode.
my country is using similar authorization for government "profile" (mobywatel - poland) that has similar to passkey implementation. you download the app on your phone, login via login+password (or other), download the certificates, and from now on you can point your camera on qrcodes to login to government websites; it requires pin/code or biometric confirmation on the phone - same as passkeys.