Do I need 10 gauge power cord if I have 10 gauge from panel?

OP,

Only when comparing to other cords. This is not a pursuit with absolutes… maybe the desire, but we live in a world of imperfection.

No.  There is no reason to match.  After all, do you know the gauge of the power line coming from the generating station to your home?   Miles of it.

Just make sure it's heavy enough to comfortably carry the power being drawn by your amps, which figure will be published by the manufacturer.  My uprated Krell KRS200s can draw up to 1.8kW per side.  I use the UK equivalent of 12 gauge from the board and the standard cord supplied by Krell, who may be presumed to know what is required.

No, you do not.

I will rephrase the question about the need for a 10 gauge power cable.

Would it be better to have a 10 gauge power cord that plugs into a 10 gauge dedicated circuit outlet?

Most things in this world we don’t really need but many a time it makes things better.