More gen­er­al­ly, can I in­sert me­dia cred­it in­for­ma­tion in­to my themes with a tem­plate tag, for in­stance on cat­e­go­ry pages?

I’m so glad you asked; you cer­tain­ly can! Just call <?php get_media_credit_html($post); ?> with an attachment_id (int) or post ob­ject for an at­tach­ment to get the me­dia cred­it, in­clud­ing a link to the au­thor page. To echo the re­sults, call <?php the_media_credit_html($post); ?>.