Rogue sorcerer archetype

I am not sure I understand how this works. I have a rogue that gets the sorcerer archetype via the Ancient Elf heritage (Lost Omens Character Guide).

Because of the heritage, he automatically gets the ‘Sorcerer Dedication’ archetype feat. That feat gives him two cantrips (he chose occult).

So as he gains levels he gets nothing more until he takes another sorcerer archetype feat, right?

If he later chooses ‘Basic Sorcerer Spellcasting’, he gets a first level slot, picks up a 2nd level spell at 6th character level, and a 3rd at 8th character level. Right?

So, if he only chooses those two feats, at level 20 he gets 2 cantrips, 1- 1st, 1- 2nd, and 1- 3rd level spell? Only 5 spells?

I get that it shouldn’t be as good as a primary sorcerer, but a sorcerer main gets 5 cantrips and 3 first level spells. At 20th level, a sorcerer main gets 42 spells, but our guy only gets 5.

Do I have that right?