This needs to work for the text to make sense
The infusion rules (p. 12, Tasha's Cauldron of Everything) say
Whenever you finish a long rest, you can touch a nonmagical object and imbue it with one of your artificer infusions, turning it into a magic item. An infusion works on only certain kinds of objects, as specified in the infusion's description.
You are the one infusing the item. If the item has the thrown property for you, then it meets the conditions for you and you can infuse the item. This wording is about a clean as it can get to make it clear that the weapon counts as a thrown weapon with the property for you and your class abilities, instead of just mentioning a "thrown weapon".
The "for you" restricts this to your actions and abilities. Another Artificer would not be able to infuse the item, as it does not have the property for them. There is no other interpretation of this language that makes sense: If the "for you" would mean that it somehow does not have the thrown property for you, then that aspect of the feat would not do anything.
The Thrown property is what allows you to throw a weapon in the first place. PHB, p. 147:
If a weapon has the thrown property, you can throw the weapon to make a ranged attack.
If the weapon did not have the thrown property for you, you could not even throw it to make a ranged attack (at least not as a normal weapon attack; you can throw anything as an improvised weapon, with the associated downsides, thrown property or no thrown property). That clearly would make this bullet of the feat utterly useless. If you however accept that the weapon has the property to allow you to throw it, why would it not have the property to allow you to infuse it? There is no reason to treat the two class abilities differently. Either it has the property for you, or it does not.