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This sounds like a case where some of the apps files have gotten corrupted and are causing these connectivity issues. No worries, this can usually be remedied by performing a clean reinstall, so that all the necessary app data gets built anew from the ground up. To do this follow the steps here.
If that doesn't fix things, it's a good idea to also have a look at your hosts file for Spotify entries. This page explains how you can do the check.
Hope you find this useful. Let us know how you get on.
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“Music is a language that doesn’t speak in particular words. It speaks in emotions, and if it’s in the bones, it’s in the bones.” - Keith Richards
For me, it is an audio device problem - if Spotify tries to request an output device that is busy (some other application could have gotten exclusive access to it) it says it has no internet connection (like: huh?).
This might not be a problem that occurs often for most people, but I use some tools that do capture audio devices this way.