It is. Yours is acknowledging that your things are distinguishable and the other person might want one in particular.

GP's should be used when offering a specific one, like "the red one".

You did, but you aren’t specifying which.

“I bought the car” would indicate that you bought a specific one that is jointly understood.

In fact, if you had previously talked about a specific car you were thinking about buying, “I bought a car” would be a strong indicator that you bought a different vehicle than what was discussed.

Yes you bought the car yesterday - it’s the now because it’s established in the conversation.

The point is that in saying "I bought a car", you're not attempting to specify which specific car you bought. The fact that you obviously did buy a specific car isn't relevant to the grammar of this.

If the audience already has some context about which specific car you were going to buy, then you could say "I bought the car yesterday." In that case you're referring to a specific car that the audience is expected to already be familiar with.

I think some of the confusion over this seems to be coming from attempting to apply knowledge that you have to a sentence when the audience wouldn't have that knowledge.