If it is stamped on the butt plate tang and not engraved, then it is likley not a Confederate Enfield lot number.
Some regiments marked their longarms with regiment/company/rack numbers, but the 365 seems too high to be a rack number. Outside chance it could be a British Army ID marking of some kind, but not likely.
I'll have to see your photo before I can perhaps tell you more.
There is always some demand for parts of original longarms used in the Civil War. Interest would depend on type of buttplate, condition, etc. While there may be some folks who collect buttplates, most would primarily be interested in an original buttplate if it was still in good enough condition to use as a replacement part on an original weapon.
If you send me photos of markings on the other buttplates, I will try to determine what if any significance they may have.