Photos - items have not been uploaded to iCloud

Hello people!

I am dealing with the following issue all day long, red lots of info on Google and the current forum.

Basically I have an iPhone SE (iOS 11.3) and my free iCloud storage (5GB) is full.
I have the "430 items have not been uploaded to iCloud" message when I open the Photos application.
I upgraded the iCloud storage to 50GB ($0.99) and waited for several hours already (5-6), but still the Photos do not sync to iCloud.

I have not tried to disable/enable iCloud Photo Library (Settings > Photos) or sign out/sign in to iCloud (Settings > [Name] > Sign Out), because I am afraid that the currently not sync-ed photos will be deleted from my iPhone.

Unfortunately when I try to get chat support I am referred to Support page in my home country language (Bulgarian), where contact carrier and contact repair service are only available. Considering the fact that my carrier support is worse than monkeys I do not want to waste my time on that path.

I am looking forward to your thoughts and recommendations!
I will be very happy if Apple Support Specialist can comment on that case.