I don't use an Android phone, so I don't know how photos are tagged there. I just did some tests with some photos that had been uploaded to Google Photos from my iPhone. Although I can perform a search in Google Photos and retrieve items such as "red flowers", if I download those files to my computer and import them into the Organizer, there is no metadata available. Nor are there any tags that are available via Windows File Explorer file properties. Similarly, Google has a name added to some of my photos and I was able to confirm other faces were the same person in Google Photos. But when I downloaded those files to my computer and imported them, no name tags were applied.
So, the simple answer is that any tags or search terms that can be found on your phone or via Google Photos do not get transferred when imported to the Organizer.
Similarly, even if you write metadata tags to the file in the Organizer, there is not really a way to view those across different platforms, although some may be viewable in some programs. For example, Organizer tags and captions can be viewed in file properties in Win Explorer.
Personally, I import files from numerous cameras and phones and other sources to my Organizer catalog. The automatically generated smart tags work well for me when used with the Organizer's search facility and I have not been so fastidious with keyword tagging my photos because the search facility is so good. However, I do use face recognition extensively to tag People in my photos. I'm not sure I understand your concern about importing from multiple devices other than the need to download files from each one separately.
As far as sharing/viewing photos on a phone, Elements 2021 now has the option to save/upload your photos to the Adobe Cloud. But, it only gives you limited storage space and you have to pay extra for more.