The most I've ever had was, I think, 39, but that was with a synthetic race where approval is always at 100% and also using the Enhanced Terraforming mod to be able to terraform up to class 39.

With carbon based lifeforms, I've had populations in the middle to upper 20s at 100% approval, using stadiums, entertainment capital, supportive population tech, easy to please tech (+4 morale), etc.

Each +1 population becomes +1 raw production, which then becomes +1 social production, +1 ship construction, +1 research, and +1 income.  So population is rather important if you want your planet to be productive.

If you're asking for help on how to manage approval, please let us know what DLCs you have installed.  Crusade?  Intrigue?

Ok, if you're on Intrigue then the government type and tax rate have impacts on your approval.  If you mouse over Approval on your planet window you can see what is affecting your approval.  If your Unrest is high you might have your tax rate set too high, and if you have a Too Many Colonies penalty, you might need to change your government type to one that supports more colonies.

If you're not making enough money to lower your tax rate, are you exploiting tourism?  Building a port of call and a consulate on every planet can really cause the money to roll in later in the game, letting you lower your tax rate.  I currently have mine set at 20%

Don't forget adjacency bonus, 2 Entertainment centers next to each give a lot of approval.  As they update, they just get more powerful.  Then later you can remove them and replace them with production improvements if you like.  Please see my other post where I had 0 approval, this is how I solved it.