Liberty was the clear choice in vanilla. In G&K they buffed Tradition and nerfed Liberty, which switched their popularity in general terms.
But in terms of population growth (particularly in your capital -- which was your original question), there is simply no comparison between the two. Liberty provides no food or growth bonuses, while Tradition provides +2 food in your capital, +25% growth in your capital, +15% in all other cities, and free aqueducts in your capital and next 3 cities, all of which compound to huge growth benefits, particularly in your capital.
Took another look at your save. One other growth benefit you are not enjoying is maritime CS friends and allies. A maritime friend provides +2 base food in your capital, and allies provide another +1 food in your capital and each other city. You have met 4 maritimes, and are allied with one (+3 food in your capital ), but are not friends with any of the other three -- Austria is allied with two, while the Netherlands is allied with the last one, and could be a friend of the other three -- if so, that's a total of +9 food in Amsterdam, which is huge.
On terrain, I don't think that has been as great a factor as you might believe. At 15 pop you still haven't felt the impact of the mountain range, so that hasn't affected your growth yet (but ultimately would if your pop got high enough). The overall terrain is OK -- you only have one bonus food tile (the bananas), which is unfortunate (FWIW, Amsterdam also only has one bonus food tile (wheat)), but you do have plenty of river for post-Civil Service farm bonuses. I would quibble with some of your choices -- I would have farmed the riverside hill next to the city center, rather than mining it, and I would have cleared at least a couple of the river-side jungle tiles for farms, but that's just me.
On jungle tiles, I know many believe they should never be cleared, since with a university and a TP you get a tile that is self-sustaining (2 food) and produces gold and science (more with Free Thought, but you haven't opened Rationalism yet). But self-sustaining means they aren't contributing to growth. I'm not a big fan of TP spam in my capital, but again that's just me.
On the recently founded cities, grabbing strategic resources is a good reason, but then you need to improve the resources. You don't have nearly enough workers, and the two you do have are doing low-priority improvements in one city (TPs in Nottingham). Buy a worker in Coventry to improve the aluminum and another in your capital to improve the coal, the riverside marsh tile (and also buy the other riverside marsh tile before Florence grabs it -- Florence, BTW, got diplo married by Austria a few turns after I loaded the save).
But in terms of population growth (particularly in your capital -- which was your original question), there is simply no comparison between the two. Liberty provides no food or growth bonuses, while Tradition provides +2 food in your capital, +25% growth in your capital, +15% in all other cities, and free aqueducts in your capital and next 3 cities, all of which compound to huge growth benefits, particularly in your capital.
Took another look at your save. One other growth benefit you are not enjoying is maritime CS friends and allies. A maritime friend provides +2 base food in your capital, and allies provide another +1 food in your capital and each other city. You have met 4 maritimes, and are allied with one (+3 food in your capital ), but are not friends with any of the other three -- Austria is allied with two, while the Netherlands is allied with the last one, and could be a friend of the other three -- if so, that's a total of +9 food in Amsterdam, which is huge.
On terrain, I don't think that has been as great a factor as you might believe. At 15 pop you still haven't felt the impact of the mountain range, so that hasn't affected your growth yet (but ultimately would if your pop got high enough). The overall terrain is OK -- you only have one bonus food tile (the bananas), which is unfortunate (FWIW, Amsterdam also only has one bonus food tile (wheat)), but you do have plenty of river for post-Civil Service farm bonuses. I would quibble with some of your choices -- I would have farmed the riverside hill next to the city center, rather than mining it, and I would have cleared at least a couple of the river-side jungle tiles for farms, but that's just me.
On jungle tiles, I know many believe they should never be cleared, since with a university and a TP you get a tile that is self-sustaining (2 food) and produces gold and science (more with Free Thought, but you haven't opened Rationalism yet). But self-sustaining means they aren't contributing to growth. I'm not a big fan of TP spam in my capital, but again that's just me.
On the recently founded cities, grabbing strategic resources is a good reason, but then you need to improve the resources. You don't have nearly enough workers, and the two you do have are doing low-priority improvements in one city (TPs in Nottingham). Buy a worker in Coventry to improve the aluminum and another in your capital to improve the coal, the riverside marsh tile (and also buy the other riverside marsh tile before Florence grabs it -- Florence, BTW, got diplo married by Austria a few turns after I loaded the save).