Does someone have a chart of what classes, races and spells are in the different source books?  Every time I go looking I see descriptions that say "has 9 classes and 3 races".  That's great, what races?  What classes?  Where's the list?

In the marketplace, click title of the book. Scroll down. You can just go to the Sources menu in the top of any page, click one, and in the Contents Page you will see a section for character options, if the book offers any, and what options. You can view the contents page even if you don't have that book.

Addition:

Games Rules in menu and then choose Races, Feats, etc. It will then take you to a page listing all of them on D&D Beyond. Clicking one will either display it, if you have access to it, or take you to the relevant book in the marketplace for buying it (or the book). Races already organises everything by sourcebook.

I was going to make a spreadsheet but going through every source - sourcebook and adventures - to list everything would take far too long. Given that it you can find out how to unlock whatever you need in 3 clicks or less, it also seemed like a waste of time. 

So you're telling me no, there is no single location, I have to look at each book separately and check each list.  Or check each subclass or check each spell.

Has no one heard of an index?

No, I am saying that if you take 20 seconds to go to the right page and click a couple things, you will have a semi-index.

If you go to the pages, such as Races, Feats, etc from the Game Rules menu, it will either already list them by source or let you filter by source. If you see something you think you might like, click it and it will take you to the details if you have access to it, or to the book in the marketplace to buy it.

It's not an ideal way, but it does the job. Best ya got. ¯\_(ツ)_/¯

The spells page doesn't list sources, you have to check each spell, or filter by a source, the classes page doesn't list subclasses, the races page doesn't list the subrace sources.

So no, there isn't a list, there are just ways to go find out by searching.

This is a list: https://dungeonsdragons.fandom.com/wiki/List_of_Dungeons_&_Dragons_5th_edition_character_classes

This is also a list: https://www.dnd-spells.com/spells

Both are incomplete, but the point is that the actual source company selling the sources, apparently doesn't want a complete list.