SSPR is configured per user, the computer/device does not matter here. In addition, there is no functionality to directly exclude a user from SSPR requirements. Instead, you need to do it the other way around - define a group on members of which the SSPR requirements will be enforced, and do not add the user(s) you want to exclude as members of the group.
The process isn't very flexible, as only a single group can be specified, and only in "include" mode, but it should be sufficient to address your scenario. Details are here if you need them: https://learn.microsoft.com/en-us/entra/identity/authentication/tutorial-enable-sspr#enable-self-service-password-reset