How does one gain access to Hebrew Cantillation diagrams in Logos?

They are included in the Logos Max subscription.

Thanks! Unfortunate there's not another way to access it, everyone wants that subscription money nowadays. This software is a bit of a money pit!

Technically, there is still a way to purchase the Logos 10 full feature set, which includes the cantillation analysis databases:
https://www.logos.com/product/228527/conjunto-completo-de-funcionalidades-verbum-10-em-portugues
https://www.logos.com/product/228533/verbum-10-espanol-conjunto-completo-de-funcionalidades
https://www.logos.com/product/229702/verbum-10-bilingue-espanol-english-conjunto-completo-de-funcionalidades
The cheapest of these will cost $370 or less if you already own some of the features/resources.

They are included in the Logos Max subscription.