Okay, so
Quill18 in his Part 2 Video opened up the Government screen after unlocking the first real governments with the
Civic "Political Philosophy".
As we gathered previously, we start with Chiefdom. The first governments to be unlocked after that are Autocracy, Classical Republic, and Oligarchy. Then, later you gain access to Monarchy, Merchant Republic, and Theocracy.
Each government after Chiefdom has a static bonus. However, underneath that there is a another bonus that in the video says 0% (Effect bonus). This is conjecture, but I believe this is the "Government Legacy Bonuses" that is referenced in America's Civilization Unique Ability.
Here's what I could grab from the video. Question marks (?) denote unconfirmed info. Ellipses denotes incomplete words or phrases.
[Chiefdom]
1 Military and 1 Economic Policy slot
No other bonus
[Autocracy]
2 Military, 1 Economic, 1 Wildcard Policy slot
Capital receives +1 boost to all yields
0% Bonus on Wonder Production
[Classical Republic]
2 Economic, 1 Political, 1 Wildcard Policy slot
All cities with a district receive +1 Amenity
+0% Bonus great people point generation
[Oligarchy]
1 Military, 1 Economic, 1 Political, 1 Wildcard Policy slot
All melee units gain +4 combat strength.
+0% Combat experience for units.
[Monarchy]
3 Military, 1 Economic, 1 Political, 1 Wildcard? Policy slots
+2 Housing in any city with m[...]
+0% Bonus influence points[...]
[Merchant Republic]
1 Military, 2 Economic, 1 Political, 2 Wildcard? Policy slots
+2 Trade routes[...]
+0% Discount on Gold Purchases[...]
[Theocracy]
2 Military, 2 Economic, 1 Political?, 1 Wildcard? Policy Slots
Can buy land combat units [with...] Units +5 in Theological [Combat]
+0% Discount on Faith Purchases[...]