Do i need to press "Add to library" on Fab for every asset once I claim them for free?

If you open the individual asset page it should say you own each one, it does for me. The ones with the “owned” ticks looks like they’re the ones which have been manually added to your library. But yeah it’s a bit frustrating. As far as I know it is not necessary to add each one to the library manually, but I can’t be a 100% sure as you never know how the website functionality will change.