No, you can't just use whatever passkey manager that you want.
I use Safari, Chrome, MacOS, a Google Pixel phone, and 1Password. I have passkeys in 1Password, but it's a crap shoot if I'm able to login on a device.
Chrome wants me to use Google Password Manager. There's no option in chrome://settings to set 1Password as my passkey manager. If I try to use a passkey to login to GitHub Chrome pops up a modal that lets me choose between iCloud Keychain, Use a phone or tablet, or USB security key. There's no option to use a different credential manager.
Safari wants to use my iCloud Keychain. There's no option in MacOS Settings to set 1Password as my passkey manager. If I try to login to GitHub I get an option to Scan QR Code or Use Security key. There's no option to use a different credential manager.
My Pixel wants to use Google Password Manager. There *is* an option in Pixel Settings to set 1Password as my passkey manager, but it doesn't work in Chrome. All I can do it select "use another device" and it shows a QR code. There's no option to use a different credential manager.
Essentially every OS and browser thinks I want to use a phone for my passkey, and this is exactly the situation that I and everyone else is bothered by. I do not want to tie my login credentials to a phone that can be lost/stolen/bricked and will be replaced in several years.
So no, you can not use your own credential manager.
I use Safari, Chrome, MacOS, a Google Pixel phone, and 1Password. I have passkeys in 1Password, but it's a crap shoot if I'm able to login on a device.
Chrome wants me to use Google Password Manager. There's no option in chrome://settings to set 1Password as my passkey manager. If I try to use a passkey to login to GitHub Chrome pops up a modal that lets me choose between iCloud Keychain, Use a phone or tablet, or USB security key. There's no option to use a different credential manager.
Safari wants to use my iCloud Keychain. There's no option in MacOS Settings to set 1Password as my passkey manager. If I try to login to GitHub I get an option to Scan QR Code or Use Security key. There's no option to use a different credential manager.
My Pixel wants to use Google Password Manager. There *is* an option in Pixel Settings to set 1Password as my passkey manager, but it doesn't work in Chrome. All I can do it select "use another device" and it shows a QR code. There's no option to use a different credential manager.
Essentially every OS and browser thinks I want to use a phone for my passkey, and this is exactly the situation that I and everyone else is bothered by. I do not want to tie my login credentials to a phone that can be lost/stolen/bricked and will be replaced in several years.
So no, you can not use your own credential manager.