Lomb-Scargle periodograms: Follow-up of enabling fit_mean=True #20843

A couple of unresolved action items from #20412

1. Enable fit_mean=True for Lomb-Scargle periodograms #20412 (comment)

@astrofrog: @jakevdp suggested in https://github.com/astropy/astropy/pull/17170/changes#r1798477154 that we could pass through non-uniform errors, which is true in principle but this still fails due to a pre-existing issue on main, so I'll address in a follow-up PR to keep this one focused.

2. Enable fit_mean=True for Lomb-Scargle periodograms #20412 (comment)

@dhomeier: So you want to keep treating the cast to int version as test reference?

p.s. If you submit PR, can the branch be named mean_grams? 😆