Yes, for reference the capability of the Delta IV Heavy [0] (which launched the Parker Solar probe) is ~28,000 kg in to LEO. And the Parker solar probe [1] was only 685 kg. I don't know how close to the limit of the mass this is to get in to this orbit, but it still gives you an idea of the capability to get something to the Sun versus in to LEO.

[0] https://en.wikipedia.org/wiki/Delta_IV_Heavy

[1] https://en.wikipedia.org/wiki/Parker_Solar_Probe

Going to the sun is easy, going there fast is hard. You could put a tiny ion thruster on it and get it there in a million years

It is, indeed, way cheaper to fling it into space beyond the solar system with the right planetary alignment.

We don't actually much care about when trash would hit the sun. But yes, it's a huge delta v compared to just getting to orbit.

Adding a long duration deep space maneuvering system to allow the trash to precisely navigate the necessary gravity assists would also be far from feasibly economical.