First, an important introduction with potentially relevant details: I've been maintaining some sourdough at home for several months now, initially made from organic white bread flour, then from half organic barley flour (I think it's white but it's significantly courser than the wheat or bread flour) and half organic white bread flour.
Almost all the recipes I checked online would instruct to take half of the dough for baking after 24 hours, then top up the sourdough with the same total weight of equal weights of water and flour. And in the beginning, I took that literally, so I'd take out half of the dough, add some salt and a dash of olive oil to it and mix, then bake it after heating the oven for a while. However, because of mixing the oil and salt with the dough, all the bubbles would be gone, and the bread was never fluffy.
After a few months, I did some testing and noticed that the dough stops rising after about 5 hours. So I changed the way I do things and started to top up the dough with new water and flour first, then take out some of that half-fresh dough for baking, salt it and leave it in the baking tray for about 4 hours, then put it in the oven. And that indeed started to produce softer, fluffier bread.
However, this means that about half of the bread I eat is made from dough that hasn't fermented for 24 hours. So now I find myself wondering ...
How do bakeries produce such soft, fluffy sourdough bread that tastes wholly like sourdough bread? And how can I do the same if my dough literally stops rising after roughly just 5 hours? How do I "take out half of the sourdough for baking" exactly? How do I add salt and a dash of oil to it without doing away with all the bubbles that constitute the fluffiness?
Thank you for any tips and help.
EDIT & UPDATE: I've waited long enough to pick an answer and feel forced now to just do it. I was waiting for two things: the results of my own experimentation with some of my findings from the comments and answers here, and to see whether the upvotes can help me pick an answer (it's really hard for me). Unfortunately, the votes are all equal on 3 answers at the time of this update, so it falls solely to me to pick an answer at this point. However, regardless of what I pick, I want to share part of the answer as my own findings, and I'm nowhere near cheeky enough to answer my own question as the newbie I am in this field:
I found out that, indeed, an important concept to understand is to treat the sourdough as the starter or leavening agent of the bread recipe that one bakes. And perhaps to never make the sourdough more than 50% of the total weight of the bread dough that one will bake.
I also realized that most "proper" sourdough bread recipes add significantly more flour than water. In other words, the ratio of flour to water is usually significantly higher than 1:1.
And I found out that, for whatever reason, I simply couldn't bake bread that was soft and fluffy enough in the inside by using such ratios that really favor the flour. The bread that such recipes produced for me was "meaty", or it was very filling, but it also wasn't as soft and fluffy as I wanted.
I found out that I find more success producing the bread I want by keeping the ratio of flour to water close to 1:1 but I'm still playing around with ratios of flour to water around 1.1:1. I'm still decreasing the flour to a ratio of 1.05 and increasing it to 1.15 to keep experimenting until I hit the perfect spot for my liking one day, hopefully.
Keeping the weight of the flour close to the weight of the water this way also has the added benefit of enabling me to use a normal, cheap hand mixer to "knead" the dough, instead of being forced to knead by hand or buy a very expensive kitchen dough mixer.
And by way of that, I found out that you really have to knead the dough long enough for it to turn glue or gum-like in order for it to reach the right structure that allows it to hold its bubbles well, and also to feel soft and smooth in the inside after baking. And this is where a ratio of 1.1 flour to 1 water, enabling the use of a hand mixer, really shines for me.
Finally, I thank all those who helped me reach those conclusions and understandings by comments and answers here.