Definition of Electronic energy
Electronic energy is indeed an eigenvalue of electronic Hamiltonian, and, as you correctly pointed out, it doesn't include the contribution from repulsions of the fixed nuclei (which has nothing to do with electrons). But sometimes the total energy for a particular nuclear configuration (one that includes the above mentioned interactions contribution) is still (incorrectly) termed "electronic energy" while just an eigenvalue of electronic Hamiltonian is called "pure electronic energy". That is essentially wrong, but it is sort of a custom.

And I would not say that "all the electronic structure packages quote the Total energy as the electronic energy". Did you check all of them? For instance, I quickly checked one of my DALTON calculations, and found this:


@    Final DFT energy:           -210.248305383291                 
@    Nuclear repulsion:           158.997839473485
@    Electronic energy:          -369.246144856776



So the first one is the (total) energy, then come its two components with the right names.

Same for ORCA:


Total Energy       :         -210.25104538 Eh           -5721.22181 eV

Components:
Nuclear Repulsion  :          158.99783872 Eh            4326.55115 eV
Electronic Energy  :         -369.24888411 Eh          -10047.77296 eV



GAMESS-US (here first two terms = electronic energy)


        ONE ELECTRON ENERGY =    -596.6619030866
        TWO ELECTRON ENERGY =     228.7817683952
   NUCLEAR REPULSION ENERGY =     158.9978510234
                              ------------------
               TOTAL ENERGY =    -208.8822836680



NWChem (middle three terms = electronic energy)


         Total DFT energy =     -210.248032406037
      One electron energy =     -597.377034042581
           Coulomb energy =      258.596296569204
    Exchange-Corr. energy =      -30.465145956066
 Nuclear repulsion energy =      158.997851023405



And I don't want to continue, since I'm pretty sure that most of the programs use the right terms.