Mac Photos

I’m not sure I usually just do a back up on the computer when it askes me.

Are you using Time Machine? Time Machine will start nagging, if you did not backup in a long time.

To restore from your Time Machine backups, see: https://support.apple.com/HT201250

Time Machine will usually only show backups from your current computer. To restore from a Time Machine backup from a different computer, you have to use the time machine menulette in the main menu bar. If you hold down the options key while launching Time Machine from the main menu bar, it will show an entry "Browse other backup disks", and you can browse the backups from a different Mac, if the drive is connected.

If Time Machine does not show in the main menu bar, enable it in System Preferences > Time Machine > Show in Menu bar.

I thought I could log into my new Mac and someone it would transfer it over like a Drop box.

If you have your photos on Dropbox then you can get them from there

Likewise if you have your photos on iCloud Photo Library

There is no automatic magic that is going to happen - you have to make off site copies and/or backups if your photos are valuable to you otherwise you wil lose them when you have a problem like this

LN

How do you have them backed up? Basically you restore he backup to the new computer if your existing system hard drive is not able to operate

LN