As title says. They are added to prepared spells and not the spellbook. They are not prepared at all times spells either, or once a day spells. Not really a big issue, but it should be noted and fixed.

I noticed this also, and it ends up allowing me to prepare more spells than I think I should be able to....

They come up as available to cast, but they are not actually counted against how many prepared spells I can have nor do they show as being learned and in my spellbook. 

This is still a bug as of today, I noticed it right away for my level 3 Illusion Savant. I presume as I get further free spells via Savant (e.g. when unlocking level 3 spells) this prepared count will just get further "off". I've just added them into my spell book, and only "prepared" 4/6. 

This bug still here.

further more, once I hit lvl5 I can't select an additional spell as part of this feature in D&D Beyond

I've just added them into my spell book, and only "prepared" 4/6. 

This is all well and good, if you actually want the spells from Savant prepared for the day, but sometimes you want other spells prepared instead.🤷‍♂️

There are so many bugs regarding spellcasting features in ddb.  e.g. Many of the feats that grant you spellcasting (Fey Touched, Magic Initiate, etc.) say that the granted spells are "always prepared" and can be cast with spell slots in addition to the 1/long rest that you get for free.  But they don't get added to your prepared spells, so you get the free "Use" option, but not the slotted "Cast" option.

And to make matters even more confusing, some feats are half right, and half wrong.  e.g. Fey Touched gives you both "Cast" and "Use" for Misty Step, but only gives you "Use" for the 1st level spell you select for the feat. 😭