Hard Drive Too Small. Need help on how to manage

Due to my own stupidity, I bought a powerful Mac Mini with a too-small 128GB hard drive. (I can’t change it as I didn’t buy it from Apple.)

Rather than sell 2018 Mac Mini and lose mucho money, I bought a G-Tech SSD just for my photos and videos as Apple tell me the 128GB hard drive can handle everything else I need.

How do I move my photo library from my old 500GB Mac Mini’s Time Machine backup—which is on its own external drive—to the new external drive, then put the rest of the back up (documents and the OS, etc.) onto the new Mini’s hard drive?

Can I manually choose what goes where?

Also, if I do put the Photos folder on the G-Tech drive and keep it mounted, will it automatically use the operating system on the new Mac Mini hard drive to open the folder?

Thanks for any help.