I was focused on running a cottage economy this game - hence the Liberalism despite Hannibal having it.
I think it is detrimental to classify a given game as 'cottage economy' or 'specialist economy'. It can lead you to do things that theoretically synnergise, at the expense of 'playing the map'.
The theory would be that more cottages = free speech better BUT Bureacracy is often still preferred from a strictly science perspective until you have a LOT of towns. In particular, this is because Burea is one of the few *multiplicative multipliers* in the game. ie: a simple capital with 75 base commerce turn (say, 7 towns, 3 trade routes of 4 each, and some windmills/luxury resources /river tiles), and 75% base science modifiers up to Astronomy (Lib, Uni, Observatory, ignoring the potential for Oxford or an Acadamy or monastaries) is worth about 75 * 1.75 = 130ish science/ turn.
With Burea, that becomes 75 *1.5 * 1.75 = 180ish science / turn. With free speech adding 14 base commerce, that becomes 89 * 1.75 = about 155ish science turn. To make up the 25 lost science compared to burea, assuming avg 50% science modifiers in the rest of your empire, you'd need another 8-9 towns elsewhere, before factoring the hammers from Burea or the ability to forgo modifer buildings in other cities or the ability to academy or oxford your capital. Additionally in your case you need to factor the 1500isb beaker investment into Lib to get free speech in the first place.
If all your villages in the screenshots were towns already, and only 7 were in your capital, beakers /turn between burea and free speech is about brekeven, before considering the time investment to get there.