When I wrote this answer, it was borderline a true answer to the question. With a recent question edit, it doesn't really answer it all. I'll leave it up as a legacy answer, unless there's a movement to delete it.
I'm trying to think of any relevant personal experience (or that of someone I know well) I have to share about similar situations, and I don't. Then I thought that the person who does is you. What did you negotiate for the current series (not asking for details you don't want to share)? We know the copyright arrangement. Flat fee? royalties? both? Though I would assume they'd pay you, not you them. Any take (from advertising) would be on their end, no?
One writer I know of who has her own successful advice column/blog who also writes for known online sites is Alison Green of Ask a Manager. She uses the term "brand partnership."
Brand partnership, or co-branding, is a popular marketing
technique used to transfer the success of one brand to the partnered
brands. With co-branding, one partner offers their branded product in
conjunction with another company's branded product, such as a fast
food restaurant offering a branded toy with a meal. Co-branding can
also occur when the partners physically combined their separate
branded products to create a new and unique product shared by the
partners, such as mixing a branded toothpaste with a branded
mouthwash. The separate brands don't need to be equal in the
marketplace, but the relationship should be obvious to consumers.
Some people simply get paid for articles they write that are published online or on paper. In her case, she's collaborating with magazines like Inc. and Slate to leverage her brand and their brand to mutual advantage. I have zero idea of the payment arrangements, but she appears to retain copyright (the questions, but not answers, still appear on her blog).
I can't imagine any site that would charge someone for providing content, with the exception of an outright advertisement. As a website creator, I've over the years received offers from companies to allow them to pay me to put up an article they've written, one that highlights and promotes their product. Because they specifically wanted their article to be on the same level as the neutral articles I wrote myself (or got permission to use from from mailing list users), I always turned them down. (This was before online ads were easy peasy to set up so I did a few manually but really didn't explore my options, much to my regret.)
If you're providing actual content (and the link to your current work confirms it), websites and other locations won't be out to do you a favor. If the content is something they want, they'll "purchase" it. In quotes because most will offer you a big fat nothing, except eyeballs. Publishers in paper will offer you copies. But some will pay. Here's a new online zine with some serious money.
You're the author, you retain copyright unless you specifically sign it away in your contract, and payment can be a flat fee or royalties or both, depending on what you negotiate, but more likely a flat fee.