I purchased the PHB using the dnd beyond  mobile app and it hasn’t shown on the actual website. I can use it on the app fine. I assumed that if you purchase it on mobile it would show on on the actual website account since they’re linked but this is not the case. Is there something wrong with the transferring of data from app to website?

First, make absolutely certain that you are signed in on the same account in both places.  It is unbelievably common for folks to inadvertently have multiple accounts here.

Second, while on the website, check to see if your entitlements are in sync.  Tap on or hover over your user name in the upper right of this page.  Select Account, then click on the Marketplace tab.  Check what it says under "Account Entitlements."  If it suggests you need to sync, tap the sync button.

While you are there, scroll down and take a look at the "Current Produc Licenses" section to see if the PHB is there.

If none of those work, contact support by clicking on the "Contact us" line below.