Does not upgrading city limit population growth?

[Emx77]

My understanding is that city upgrade does not limit natural population growth. In manual it is stated:

5.3.10. DemographIcs

There is natural Populace growth, but this growth is quite slow. Natural population growth is positively modified by Fertility of the culture of the Zone and the Health Score. It is negatively impact by a high Civilisation Score." (p. 177)

However in his recent YT playthrough Das said:

"Essentialy the smaller the town the happier population will be to a degree but they won't grow quickly and really the growth is very very important. So when you have got a zone that is happy - uprade. It is essentialy rule of thumb."

Usually, I would upgrade city only when I need higher tier buildings. However, as game progress, I've noticed problem with not having enough workers to operate upgraded public assets. Could it be that, beside factors mentioned in manual which are related to population growth, there could be some additional hard limits linked directly with city level itself?

[eddieballgame]

I, too, don't upgrade too early unless to build the higher tier buildings; (early game 'PPs' can be scarce, as well) does not appear to affect growth...but it might have some impact.
The natural migration of pop due to jobs or lack of, etc can be aided via sending available colonists for jobs that are short workers.

[Emx77]

This is from manual (p. 165):

The City Level is an indication of the City’s infrastructure and administration. It does not limit Population, but it does limit the Level that Public Assets can reach.

And that answers my question.

[eddieballgame]

One thing is fairly certain, as your cities get upgraded to allow for upgraded (better) facilities...more folks should want to migrate there, based on work & a decent wage.
Per the Manual, starting at: 5.3.8.1. Population Growth from Free Folk, thru 5.3.8.3. is worth a look.
This addresses key issues like happiness, hunger, & exposure.