The "Locate Object" spell says that you can locate an object that you are familiar with within 1,000 feet.
Then it gives an alternate use that you can locate the closest object of a type, but doesn't specify a range.
The question is: Is the alternative use unlimited in distance (up to the nearest object of that kind) or is it still limited to 1,000 feet?
You seem to parsing this like this
Where you seem to miss where the paragraphs are broken.
Object you know:
Describe or name an object that is familiar to you. You sense the direction to the object’s location, as long as that object is within 1,000 feet of you. If the object is in motion, you know the direction of its movement. The spell can locate a specific object known to you, as long as you have seen it up close – within 30 feet – at least once.
Object of a kind:
Alternatively, the spell can locate the nearest object of a particular kind, such as a certain kind of apparel, jewelry, furniture, tool, or weapon. This spell can’t locate an object if any thickness of lead, even a thin sheet, blocks a direct path between you and the object.
I'd argue the proper parsing is like this
As it shows in the paragraph break between the top general rules and then two specific rules. General rules applying to both uses:
Describe or name an object that is familiar to you. You sense the direction to the object’s location, as long as that object is within 1,000 feet of you. If the object is in motion, you know the direction of its movement.
Here is where there is a paragraph break. Everything above this is a complete thought in the English language. The following two sentences share a paragraph and are two sides of the same thought.
Game designers and authors choose carefully where to place breaks in their text to create clarity.
A Specific object rule:
The spell can locate a specific object known to you, as long as you have seen it up close – within 30 feet – at least once.
The specific kind of object rule:
Alternatively, the spell can locate the nearest object of a particular kind, such as a certain kind of apparel, jewelry, furniture, tool, or weapon. This spell can’t locate an object if any thickness of lead, even a thin sheet, blocks a direct path between you and the object.
The way that is written is correct, and clear. This can be demonstrated by taking out the rules for a specific object all together and reading it:
Describe or name an object that is familiar to you. You sense the direction to the object's location, as lang as that object is within 1,000 feet of you. If the object is in motion, you know the direction of its movement.
... [T]he spell can locate the nearest object of a particular kind, such as a certain kind of apparel, jewelry, furniture, tool, or weapon.
Thus, you end up with what happens in the case of kind of object. You say the magic words, then describe the kind of object ("jewelry"), and then you sense the direction to the nearest object of that kind that is within 1,000 feet of you, and know what direction it is moving in if it is moving.
"If that's the case why didn't they just make the range 1000ft?"
I'd wager it is because the affected target is the caster, not the object or area it cast in. That way the 1000ft moves with the caster. Since the spell has a 10 minute duration, and the average PC has a movement of at least 30ft per round, and 10 minutes is 600 rounds, having the area affect left behind would nerf the spell to uselessness.
Moreover, the range is for targeting not the extent of the effects. An example of this is teleport where it has a range of 10 ft for the target but the limit to where you can arrive at is anywhere on the plane that you know.
