The item to which I added media didn’t show up in the site at all, so not when browsing through all items and not when searching for the content of the fields of this particular item.
But in the meantime I solved the matter: I am running Omeka-S v4.1.1 on shared hosting and when starting to add media to items I already entered, I ran into an error, which I could solve by changing “ImageMagick” in one of the lines of the local.config.php file into “Imagick” (following this post).
Then - euphoric about this success - I picked one item to add media to for testing purposes, which - as it now appears - wasn’t connected to the site, sorry, my bad.
I have created several item sets, but only one of them is connected to the site, so when adding items to other item sets I have to specifically not connect those to the site, hence the confusion.
Maybe such a confusion could be avoided in case a) it would be possible to duplicate the basics of the previously created item (which item set, which resource template, which site), when creating a few of the same sort of items in row (so as a result of confirming the question: “Add another item?”), or b) to add more parameters like this when creating item sets. But maybe there is already such functionality in place and I am simply not aware of it?
Best,
Jan