(esp. for tradition as it has the least science in its tree)
That's Authority, unless you're really snowballing in your wars and barb hunts. Tradition has good science in the long run due to the extra scientist slot, +10% yields at the Capital and access to the University of Sankore. With the latter, Tradition even compares favorably with Progress. It's just that Tradition gets its science much later and isn't designed around rewarding science like Progress is (culture on techs, infrastructure bonuses to actually make use of what your techs unlock).
Artistry's policies usually focus on things related to

great works. More yields from Humanism, multiple bonuses related to guilds and buildings that store great works (Amphitheater, Opera House, World Wonders), and the ability to see Hidden antiquity sites. It also has four ways to boost

Golden Ages (scaler, Heritage, Cultural Exchange, finisher), so GAs are a focus as well. I think those are already enough focuses for a single tree, I don't think it should go too heavy on other things, such as

science and non-cultural

GPs.
Making it give more culture or science and production is a way of making it available for progress too, which is now very weak and still be troublesome combo, and more consistent for authority, which is very situational.
The abundance of

culture and frequent

GAs are already quite strong, honestly. This is the tree to go for in order to achieve permanent

GAs. If you want it to be better for Progress and Authority, it is enough to move Cultural Exchange's "+2

Culture and

Production to Amphitheaters and Opera Houses" to an earlier policy, such as Refinement. It is the main infrastructure bonus of the tree and is currently among the last ones you can pick.
Progress would also benefit from Artistry giving a bonus towards archaeologists, since the tree is focused on science and tends to unlock them before Tradition and Authority rivals.
Here is what I propose:
Tradition
Splendor - Expending a

Great Person grants 50

Culture (currently 50

Golden Age Points
and 
Culture)
Finisher - Add +1 City working range. Remove +25%

Golden Age length
Artistry
Opener - Add Earn Great Artists, Writers, and Musicians +25% faster. Remove +25%

Great Person Rate in all Cities
Scaler - +2

Golden Age Points in all cities and -5%

Golden Age Meter size. (ie. shrinks the number of GAP needed to trigger golden ages by 5% per policy. remove +1

in all cities)
National Treasure - Free Great Person of your choice. 33% of
Happiness produced in each City is added to the City's

Science per Turn. (used to be 50

gold for GP expend. happiness to science works the same as fealty's happiness to culture)
I think this proposal is an overall nerf to both trees, which I don't think they need. I'd go with something like this:
Tradition
Opener - 4

food in the

Capital instead of 2

food.
Scaler - add "+1

food in the

Capital".
Splendor - Remove the 50

Golden Age Points from GP expenditure.
Finisher - Add +1 City working range. Remove +25%

Golden Age length.
Artistry
Opener - Change the "+25%

Great Person Rate" to "Earn Great Artists, Writers, and Musicians +33% faster".
National Treasure - Replace the

gold from

GP expenditure with "Archaeologists gain +1

Movement and are trained 100%

faster".
Refinement - Gain "+2

Culture and

Production to Amphitheaters and Opera Houses".
Cultural Heritage - Loses "+2

Culture and

Production to Amphitheaters and Opera Houses".