Maxima 5.31.0 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
(%i2) display2d:false
(%i3) load(to_poly_solve)
(%i4) %solve(z+z*conjugate(z) = 23,z,'simpfuncs = ['expand])
(%o4) %union([z = -sqrt(93)/2-1/2],[z = sqrt(93)/2-1/2])
(%i5) declare(z,complex)
(%o5) done
(%i6) %solve(z+z*conjugate(z) = 23,z,'simpfuncs = ['expand])
(%o6) %union()
Maxima 5.31.0 http://maxima.sourceforge.net
using Lisp SBCL 1.1.1
(%i2) display2d:false
(%i3) load(to_poly_solve)
(%i4) %solve(z+z*conjugate(z) = 23,z,'simpfuncs = ['expand])
(%o4) %union([z = -sqrt(93)/2-1/2],[z = sqrt(93)/2-1/2])
(%i5) declare(z,complex)
(%o5) done
(%i6) %solve(z+z*conjugate(z) = 23,z,'simpfuncs = ['expand])
(%o6) %union([z = -sqrt(93)/2-1/2],[z = sqrt(93)/2-1/2])
(%o6) "/home/jlapeyre/maxima/mext/tpdemo2.mac"

The test suite says that the solution should be found with

declare(z,complex). The gcl maxima fails the test suite for this

reason, when run from the command line. But, when I built the gcl build, all rtests passed.

Don't know why.