I really don’t think there is going to be a monarchy. Its unclear if a monarchy was ever intended for Israel in the first place, and it is clear from Navi (gasp, i read the rest of the torah other than the first five books) that all monarchies ended in disaster.
No reason the new moshiach state can’t be a democracy. Sure the sources don’t mention a democracy, but since the concept didnt exist at the time you would hardly expect it to be talked about.
I would just read all references to kings as references to government powers which could be a democracy as well.