I know how to do a PES scan for a ground electronic state. But for the nth-excited state, is it the same (i.e. an excited state optimization and just rotating the dihedral to simulate the isomerization)? Is it essentially a separate PES, or do I use my ground state geometries and do excited state optimizations on them?
My understanding is that you just define your internal coordinates, and then do SP calculations (and maybe thermodynamic correct at critical points) at the ground state.
To scan the potential energy surface (PES) for an excited electronic state, you can do the same thing that you would do for scanning the PES for the ground electronic state, except that you need to ensure that your calculations are targeting the excited state.
In software such as mrcc and pyscf, when using CCSD(T) or CISD or any of the electronic structure methods that I typically use, the user can specify the number of "roots" (usually with a variable name such as nroots), which effectively is the number of states for which you will be obtaining an energy.
Here is an example of some of my own calculations on the H2 molecule at equilibrium with the aug-cc-pVDZ basis set and the FCI (CISD = FCI for a 2-electron system) method (these are the energies of the lowest three electronic states obtained by MRCC):
MRCC PySCF
Total CISD energy [au]: -1.164624207027 -1.16462421 (1^1 Sigma_g)
Total CISD energy [au]: -0.683393683543 -0.68339368
Total CISD energy [au]: -0.427295580627 -0.42729558 (3^3 Sigma_g)
The PySCF output file (which contains the input file) can be found here, but you would likely need to use grep to organize the three above energies in the type of column array that I displayed here.
To scan the PES with the excited state, you would do the same type of calculation as done in the input file that I made available from the link in the previous paragraph, except you would do it for more geometries (i.e. different values for the internal coordinates, since you suggested that you are using internal coordinates). If by "scan" the PES you are just looking for the minimum energy, you can also execute a geometry optimization algorithm for the excited states, provided that the software that you are using allows some of that process to be automated (or you can do the optimization manually otherwise).
"Is it essentially a separate PES"
Yes, in the way we do quantum chemistry, especially with the Born-Oppenheimer model/approximation, each electronic state has its own potential energy surface.
In the example below, which is for the Na2 molecule and from this paper, you can see the potential energy curves/surfaces for many excited electronic states of the molecule.
"or do I use my ground state geometries and do excited state optimizations on them?"
No, in the above diagram, the ground state ($X^1 \Sigma_g^+$) geometry (with lowest energy) has a bond length of around 6 Bohr radii, but the first excited electronic state with $^1 \Sigma_g^+$ symmetry is the $2 ^1\Sigma_g^+$ state which has an equilibrium bond length of around 8 Bohr radii, which is quite a big difference in terms of bond lengths. Once you pick a geometry (such as the ground electronic state equilibrium geometry), you can do excited state calculations at that geometry, but then you are not "optimizing" anything, so you are not "doing optimizations on them".
