You would have four cantrips.

The general rule is that features from your race, class, archetype, or whatever, are additional to one another. Features do not stack only when explicitly noted by the rules.

PHB p.164 is about multiclassing. Not general spellcasting rules. It is saying that each spell you know from a class is tied to that class and can't be cast using the stats of the other class.

Spells cast as part of racial feature or feat is not a class spell, and multiclassing doesn't affect how they work.

Some previous feats and features already gave you spells outside your class, like Magic Initiate. These new racial feats work exactly the same way. The source of the spell tells you what stats to use.

Charisma is your spellcasting ability for all three spells.

Similar to how Infernal Legacy tells you to use the stat of the class the spell list you took from uses.

Charisma is your spellcasting ability for these spells.

Mechanically, they work the same as other non-class spells that already existed.

The Caveat: Sometimes they are Class Spells

If you pick the spell from a spell list mentioned in the class feature or feat, like Wood Elf's cantrip or Magic Initiate, then it technically is a class spell of the other class. The only thing this really changes is that if you happen to be that class you may, in addition to the one free casting, also cast it using a class spell slot. Also if you have a class feature that interacts with casting spells from the class, those would count (i.e. Metamagic, and Wizard Arcane tradition). Note that for wizard you would have to write the spell into your spellbook, and for Wizards, Druids, Paladins you'd also have it prepared in order to cast it using a slot.