Tricky Photos to External Hard Drive Question

Old Mac Mini with 1 TB hard drive started to act up, so started using 2023 Macbook Pro with 500 GB hard drive as main computer - but not enough room for my photos or music and want to put them on an external hard drive. Macbook running Ventura, and Mac Mini running Catalina or Big Sur. If I move photos to external so they'll work with the old Mac Mini, would I simply be able to connect that same drive to my Macbook Pro and select that as my Photos library running Ventura? If not, how can I best do it? The Mac Mini was getting buggy, but I'm guessing it will hold up long enough that I can upgrade it to more recent OS if needed for a smooth transition.