Softest, smoothest sounding capacitors you've tried?

Duelunds

For mainstream audiophile stuff I use MIT styrene and tin foil from the RTX series. IME all teflon/PTFE caps are very revealing, and maybe not what you are looking for. Polypropylene film and foil can be smooth and soft, not too expensive, and available. I have no experience with oil.

All of this IMO. YMMV.

Agree with Rodman99999 - you can try Takman carbon resistors.

Don't agree 100% with Eric and petg60.  All caps have coloration (every single one does) as opposed to using chokes instead of capacitors.  Agree with mickeyb - V-Cap oil caps are smooth but do allow detail to come through.

Jupiter Copper foil not our cup of tea but are slow and musical.

Not a fan of Mundorf but have used them with good results but nothing special to our ears.

Power supply I believe we used Motorola or Mitsubishi or maybe we used Mundorf I forget PS caps with musical results when we could not fit Nichicon PS caps - I am talking about the large capacitors not the ones placed on a circuit board.

Lots of responses and you have to try them out for yourself to see how they sound in your system.

Jupiter HT or VT.

@bigkidz I understand that V-caps are teflon film. Not oil.

Also have to quibble with you comment about every cap. Air-gap and vacuum dielectric have one main characteristic: clear as crystal. Of course, they are only available in small capacitances, in large packages, for huge money.