Old Mac is stuck on looking for other computers in migrating to new laptop
How can I bypass this. There are no other computers, only an iPad and phone
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On restart hold the Shift key, that should defer the startup; to let
you login and start in Safe mode. (Or ~ hold 'power key' down to
force stop the Mac, and on startup, depending on which Mac you
have there, other key-options could be used on restart.)
• How to use Safe mode on your Mac - Apple Support
https://support.apple.com/en-us/HT201262
Some can be useful to troubleshoot system, about macOS Recovery;
to access utilities to check & repair startup disk, etc. Yet Safe boot
can repair things; and after its ran for 20+ minutes, restart normally.
Hard to say why your Mac 'sees' the need to connect elsewhere.
Safe mode, once you've used instructions there, can be useful.
A good backup, would be to have a 'Time Machine' on USB
(2TB +) external hard drive; for the built-in TM utility to use.