Good question, @MortenCopenhagen
However, as the Alt text (AKA Caption) is part of the set of metadata of an image, actually there is not a way to import and display them in Connect.
This can be considered an issue, because it reduce the accessibility of Connect, and it is one of the reason why, long time ago, as you and @SholaIB may remember, I was asking for a Tool for embedding photos from other Google products , without the need to write something in HTML.
As far as I know actually you can only add your Caption under the photo.
I am making a test with a photo where I added the description in Google Photos. You may be able to see the description here, I guess: https://photos.app.goo.gl/Sa7AymmuxrkQy4C7A
Caption: Hot sandwich with pepperoni, zucchini and cheese