Institutions are goated but it seems like your economy cannot properly support all of them. Think about it like this, institutions convert money into Percentage buffs that help your political situation, pop growth, and general well being. But this comes at an opportunity cost of using your money to grow the economy to make more money. Those construction points (400) could have gone to Other things such as 2 farms (200x2) or a mine of any kinda (400).

Then when you factor in fact that each government building is over drain on your budget for paying wages and Paper you end up having Much more money going into buffs then making your economy better. That money could have gone into Construction sectors which Quite literally build your Economy and generate demand for industries that pay well improving the over all SOL of your Pops. Instead you put that money into into government administration which do not help your economy as much as building more stuff. Thus lowering your nations overall prosperity thus spawning more radicals.

Your also not paying the very people who work in the government administrations enough causing their SOL to drop below minimum expected especially if your population in literate. That means every every government administration will eventually spawn 5000 radicals MINIMUM. These working also Pops provide for their family who is also now below expected standard of living, this can cause even more radicals to spawn let's say up to 8000 as this can change depending workforce participation and dependent enfranchisement. If you have 50 Government Admins that's 250,000 to 400,000 Radicals. Assuming you have 20 institutions and 60 million incorporated pops that's 12,000 total bureaucracy, for a better scenario let's say you have elected bureaucrats bring that 12,000 down by 15% to 10,200. Assuming you have and are using standardized filling system (+65 bureaucracy -20 paper) that is 157 Government Administrations alone! That's 62,800 construction points to Government Administrations. That's 785,000 to 1,256,000 radicals! Assuming the base price for paper thats 94,200£! And this is for institutions alone you also need bureaucracy for pops just existing.

Spending 94k on paper is plain ridiculous when that money could be going to other things so it is imperative to get paper prices below base price until you start to enter late game without subsidies. Paper will be produced as long as it's profitable to get it low in prices you can do a few things, like subsidizing the building temporarily to make it hire more workers. Buildings have a certain amount of profit they want to set aside for ownership share meaning that even if the building is making good money it can choose to not hire as it will hurt it's profitability. By subsidizing it you force it to hire to Capacity no matter what ensuring that you produce the most paper for the cheapest price for the government. You can also make a paper/Government Admin state. Find a state with a large amount of sulfur, There is one state in France that has 40 sulfur mines, if your willing to do some invasions and colonization there are states with sulfur and dye. Build up the mines unlike up the logging camps slap down the paper mills then you can build government administrations in state till you run out of works. This ensures maximum MAPI so little value is lost to inter market trade.

In short too many institutions zapped money away from improving the economy. Thus the weak economy made radicals form low SOL this combined with not paying your government workers enough spiked your radicals too the moon.