Can I use a "Photos" library created with Photos 4.0 with the Photos app 3.0

No, it is not possible to open a Photos 4.0 library directly in Photos 3.0, because the upgrade to Photos 4.0 changed the format of the library. A newer version of Photos can open and upgrade a library, but an older version can no longer open a library, once it has been upgraded to a newer format. Photos is a part of the system, so you need to upgrade the system to upgrade to a new version of Photos.

If you want to keep the Photos Libraries in sync across macs with different system versions the easiest way is iCloud Photos. Enable iCloud Photos Library on both the Mojave Mac and on the High Sierra Mac (https://support.apple.com/en-gb/guide/photos/phtf5e48489c/4.0/mac/10.14). Then wait for the iCloud Libraries from both macs to upload to iCloud and merge in iCloud. The merged library will download back to both Macs. You need to subscribe to enough Cloud storage to hold the merged library. See: Downgrading a Photos Library to a Previous Version of Photos with the Help of iCloud Photos

If you only want to download the library to the Photos 3 Mac, create a new, empty library for syncing on that mac. (https://support.apple.com/en-gb/guide/photos/pht6d60b524/4.0/mac/10.14)

And make a backup copy of the Photos Libraries, before trying to sync them with iCloud.

It will be slow, yes. But it is worth the effort, if you want to work with Photos on devices with different system versions. My library has currently a size of 240GB and the upload to iCloud took more than a week.

You will be seeing a status bar below the "Moments" showing you the progress and potential problems. You may want to check this information occasionally, see: About the status bar in Photos for macOS - Apple Support

Photos is a part of the system. You can only upgrade Photos by upgrading the system.

If your mac cannot be upgraded past High Sierra you could only restore a previous version of your library from your backups.