There are two routes, and which one you take depends on whether you use sync.
With sync
If you are on the Sync or Pro plan, install Grape on the new machine and sign in. Sync pulls your notes, attachments, settings, AI content and the folders shared with you down on its own. Your folders and notes show up first, pictures fill in as they arrive, and PDFs and recordings come after them, so give the first sync time to finish on a large library.
On Lifetime, sync goes through your own Dropbox or Google Drive. Connect it on the old machine first if it is not connected yet. Then sign in on the new one, open Settings, go to Cloud Sync and connect the same Dropbox or Google Drive, and your library comes down from there. Sync with Dropbox and Sync with Google Drive have the details.
Version history and backups are not synced, so they stay on the old machine. If you want them along, move with a backup instead.
With a backup
On the old machine, open Settings, go to Backups and click Back Up beside Back Up Now. Install Grape on the new machine, copy the backup file into the grape-backups folder in Grape's application data folder there, and restore it from the same Backups tab, which lists the backups in that folder. Backups are cross platform, so a backup made on a Mac restores on Windows or Linux.
What a restore replaces
Restoring replaces the current library on that machine with the contents of the backup. On a fresh install that is exactly what you want. Grape also creates a safety backup of the current data first, just in case.
Worth checking afterwards
Open a few notes, confirm attachments load, and let indexing finish before relying on AI search on the new machine. A fresh install may also be a version behind, and Grape offers the update in the corner once it has looked.