You should look into liquid democracy or delegative democracy....its basically direct and participatory in principle, but people who don't want to participate can delegate their vote to someone else, a delegate, who acts kind of like a representative(but not exactly).

"Libertarian social democracy with a republican system"... Let's unpack that.

Republican simply means "representative democracy"

Libertarian, as I use the term, means left-libertarian or classical libertarian, harking back to libertarian socialism which sought communal-ownership of land and the abolition of wage-slavery. I call my model libertarian social democracy insofar as it involves abolishing wage-slavery through making land publicly-owned (in principle, at least) by instituting a land value tax (or ground-rent) and distributing the revenue evenly amongst the citizens as a universal basic income.

Social democracy just designates a democratic society, with a market system, but that uses taxation in order to fund welfare programs that alleviate the injustices that naturally arise under laissez-faire.