How should I hang a 35 lb pool table light from my ceiling?
You could definitely design and build structure in the attic, get threaded rods, etc., that would support this light fixture, but it would be 10 or 100 times easier to get a proper ceiling fan rated box that would do the job. In this case get one that is rated for 70 lb.

You evidently don't have the instructions for this particular fixture and may not have all the mounting parts. Generic mounting parts would probably work, but would have to be mounting parts rated for a light fixture like this and not just metal brackets that "look like" they would do the job. Go online and get instructions for this particular fixture.

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If this fixture is designed to be suspended from more than one mounting point, then simpler mountings could be used because weight would be distributed. If the fixture that is 3 ft away is controlled a wall switch and you want to use that switch for the pool table light, then that would be a much easier install. You could run a 14/2 + gnd cable (if this is a 15-A circuit but 12/2 if this is a 20-A circuit) in the attic from the existing light to a new box for the new fixture.

I would imagine that two suspension points would be sufficient and these could be 24 inches apart on adjacent joists. If so, then fairly ordinary hooks could be screwed into the joists to support the fixture and one standard electrical box placed suitably for the wiring connection. In this type of installation the box would not be used for suspension.

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You use decorative hooks like these if the chain or a carabiner at the end is large enough to go over the hook oil rubbed bronze swag hooks and you wanted a finished look or you could use heavy steel hooks for a more industrial functional look.

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Some hooks that I like are decorative hooks but there are many choices. You could even drape a wire from the other fixture under the ceiling and have a connection in shallow surface mounted box, a so called "pancake box" which could just be attached to the surface of the ceiling with screws into plastic anchors since in this installation it would not be used to support the fixture but only the chain through which the wire would be intertwined. But honesty it looks a lot better to have the wiring hidden.