Broken particle halo

Dear Blender artists,

I am trying to get higher-resolution renders for a series of old files. Looks like the original artist (who can no longer be contacted) used a halo particle effect to make the models look more massive / make fluffy tails etc., but the render result is broken. After a day of fiddling around with it, I am giving up.

This is what it’s supposed to look like:

Original render

This is what it actually looks like:

Blender file:

brownbear_idle.blend (3.5 MB)

Any pointers on how to fix this myself will be much appreciated, because I have a whole bunch of those.

Thank you for your time.