GDP should be able to vary at least in factor of 1000.
That is from 300 GDP/capita (poorest countries/after total collapse to pre-industrial level) to 300 000 GDP/capita (ultrawealthy ultra high tech country with serious space economy).

Everything, that affects GDP would affect GDP Growth.
GDP would be numerical value - it would be used to calculate GDP/Capita, which then could be normalized to 0 - 1.
Then this GDP/Capita and GDP growth rate would affect things, that GDP normally affects now.
Increasing GDP/Capita would lower GDP growth rate forcing policies, that favor more growth.
GDP growth would be from 0 to 1 representing -+ 10% yearly growth.

Logarithms and exponents would have to be used to translate between exponentially growing GDP and 0-1 simulation bounds.
Exponential effects can be approximated with Taylor approximation if exponents and logarithms are unsupported directly in equations.

Growth being between ±10% yearly and GDP/c being between 300/300 000 $ (0-1) would cover most of scenarios.

GDP/c simulation would be extremely slow to move:
Not more than 0.01 per year, even if GDP Growth is at extreme value.

GDP and GDP/c could be displayed next to population.

I second this. The game simulates productivity but this is an input to gdp and quickly pegs the economy at 100 and you cant actually grow the economy even while increasing productivity. Productivity could be represented by GDP/c and this could be slowly increased by policies. This would also differentiate countries by initializing game at a different GDP/c

Summary: productivity should be represented by GDP/c, this fraction would be a primary target of policies with limited allowed movement each year

Everything, that affects GDP would affect GDP growth rate instead.
GDP growth rate would be scaled in such way, that 1 is 5% quarterly growth (21% yearly), and 0 is 5% quarterly shrinkage.
Default value would be 0.5 - no change in growth.
GDP growth would be dampened by logistic function.
GDP should scale in such way, that 0 is 10x smaller economy and 1 is 10x bigger economy, where 0.5 is current economy size.

Some stuff would be influenced by GDP, and other by GDP growth rate.
Since population is static number, and its changes are simply simulated, then GDP is GDP per capita just scaled.
Population growth/reduction would have instant effect and very delayed effect on GDP growth.

That is:
Current effects on GDP would be 2x - 5x smaller, and would affect GDP growth rate instead.
GDP would grow/shrink linearly as long as GDP growth rate isn’t exactly 0.5 (no growth).
GDP and GDP growth rate would affect various things.
There would be long and short term impacts on GDP growth rate from population, elderly and youth percentage.

GDP growth rate would be reduced by GDP - its harder to grow already advanced economy.
Increasing economy size 10x at 5% yearly would take around 48 years.