Not sure for power conditioner my amp or not.

I feel my amp sounds better with the power conditioner as well as the picture on my television..

Since my Onkyo HT drives all the video probably best to leave it on Power Conditioner and use the other outlet for tube Pre-Amp.

In South Florida we have a love of air conditioners cycling on and off and it causes fluctuations in the power supply.  I found that my tube amplifiers were regularly needing to be re-biased.  Since incorporating a power conditioner, the amps have stabilized to the point where re-bias in almost never needed.  The amps always sounded good, I can't say that power conditioners have done much in that regard.  I have tried Niagra and first P10 and now P20.  All with similar results.  Currently using PS Audio P20.  I did read the detailed report that these things do nothing.  I believe that is true if the power coming into the wall is good, consistent etc.  They are more necessary in localities where the power fluctuates, is dirty and so forth.

I would test it your self giving each trial a week before deciding

Since OP’s amp uses an EI power transformer which does isolation already, adding a separate isolation transformer may not give any benefit.

However, if the isolation transformer is wired in balanced manner, then it can help.