Unemployment
To me unemployment is unemployment because if they were 'unemployed' by choice to do art or something they wouldn't automatically drop what they were doing and sign on to the first job available.
I'm not sure I buy that, frankly, I think at the level of abstraction Aurora works at it's fairly reasonable to say exactly this. By the same token, I can drop a newly-constructed mine on a planet surface and it will instantly fill all 50,000 job postings in a nanosecond. I can even drop a mine on a planet, load up a financial center, and all those Wall Street accountants will instantly transform into West Virginia
coal duranium miners. The abstraction of the Aurora job market is I think a working assumption here.
I hear you about such a feature messing with fledgling colonies; I imagine that unrest will only kick in when you have 10 million people as it does currently. Generally speaking, I think keeping your pops occupied should be a minor concern for the player and hope that unemployment will factor in other things like colony migration.
I do also want to note again that the start of every game, unless you customize the number of installations, will feature several millions of "unemployed". To me as a player, this is an indication that some amount of unemployed population is expected and a "good idea" - a fact which, incidentally, matches with real-world economics as a certain unemployment percentage is necessary for a healthy economy (in a developed country with unemployment payments at least) as it correlates to overall mobility of skilled workers.
All to say, I really don't like "unemployment == unrest" suggestions as it only constrains player agency both mechanically and in RP terms, in my mind.
Not-Edit: @froggiest's suggestion of a wealth cost makes a lot more sense, I actually like this a lot as it represents an investment into sustaining small colonies which are not economically viable as well as social programs in developed populations. Perhaps with a small +% boost in starting financial centers for early game balance, otherwise a great idea.
Garrison Unrest
I think there should be a cost to creating a 'fortress world' with a disproportionate amount military units present. Its too easy to give every colony a large garrison of cheap infantry units whose sheer numbers combined with entrenchment are enough to at least stall the enemy. You should have to consciously scale up and expand the garrison in line with the planet's growth OR lay down the anti-unrest infrastructure to make a 'fortress world'. Otherwise civilians aren't going to like living under a society dominated by military concerns they didn't sign up for.
Why not? Granted, many people have ideological issues with military presence and buildup, but having a military presence also requires a population to support it - not necessarily in terms of raw production (which would be forge worlds, to continue the RP analogy) but logistically - food, housing, facilities for shore leave... if a population is not ideologically opposed to a military presence which is appropriately managed, the economic benefits are arguably net-positive for that population.
Obviously your RP might differ, but that's rather my point - I'm not a huge fan of a mechanic that restricts RP, frankly. Garrison spam already has significant costs in not only GU maintenance but also opportunity cost as you really want to dedicate most of your GU production to offensive units as the army sizes required to conquer an enemy race are quite large.
MP Ground Units
MP Ground Units would be very useful in situations where you have to occupy a recently conquered planet or respond to a sudden but temporary flare-up of unrest. Their strength is how easy it is to deploy them wherever you want and how they don't draw from the civilian population. They're like Construction Brigades for unrest. Civilian Police only cover the bare minimum unrest reduction that keeps things civil when all else is stable. State Police HQs are a long-term solution to keeping things stable when things get bad but are expensive and too large to really transport. MPs are for when smeg hits the fan and you need a rapid reaction for to stabilize things NOW without worrying about efficiency.
I should clarify that I'm not as much opposed to the principle of the unit, rather how it fits with the existing units plus the suggested police HQ installation. If we have a balance between PWL infantry and police HQ installations which is in large part based on relative costs, how does a new MP capability fit in? Either it multiplies garrison efficiency proportionally to cost, in which case it's basically pointless, or it does not in which case MP capability is either pointless or strictly superior to "plain" INF+PWL. Given that INF+PWL are already the garrison/MP unit of choice, depending on how you RP it, I don't see why we need a redundant specialized unit.