When uploading a photo or several photos from Google photos to one of your folders in the cloud online, is it supposed to take several minutes for the connection to start uploading?

No I'm not sure. They have enough data connection where uploads and downloads happen correctly. I don't understand why Google photos pauses for a good minute before starts to upload to My Cloud.Sorry, but had to ask because from your picture it seems your signal is definitely not 4 bars... In any case, are any other downloads/uploads affected? Do you notice any slow browsing or data loading on other apps?
Best see, that's a good question. Since I have the old school plan I have unlimited and never try to over Wi-Fi but I guess as a test I could try. Try to remember to do that next time.Is it compressing pictures? Although I thought this was done in the cloud, though. Does it do the same while on WiFi or just on mobile data? Have you tried uninstalling/reinstalling the app?