Should I bypass my Shunyata Hydra power conditioner?

Sounds like you've answered your own question....if it sounds better, bypass it.

See what happens with the DAC and CD player next.

I have to agree with cedargrover.

Yep.  A whole lot of people have confirmed that amplifiers in particular are often not happiest plugged into power conditioners.  It can depend upon the conditioner, but most due seem to constrain the dynamic life a bit for an amp.

It is often recommended that amps not be plugged into power conditioners because it can limit the amount of electricity available to them, which sounds like what is happening to you. There are power conditioners made to have amps plugged into them.

I’d listen to your DAC and CD player with and without power conditioning (they draw less power than your amp) and decide if it’s helping or not. As with everything else audio, you have to try something in your own system to see if it works in your situation.