When refereeing a paper, stating I am not an author of suggested literature

As a reviewer, I have suggested the authors to cite one of my papers only once or twice. I apologized for doing that in the notes to the editor, and remarked that I couldn't avoid it because it was really central. I wrote nothing in the blind notes to the authors, and I write nothing when I suggest papers from other people.

I do this because of two reasons:

1. I value anonymity of peer reviewers highly, and I prefer to avoid remarks that reduce it by unnecessarily providing additional bits of information. There are already unavoidable signs such as writing style and English mistakes, and I don't want to add more.
2. I believe it is the editor's responsibility to make sure that the referees are not citation-shopping. It can't be anyone else's, because they are the only person with all the information necessary to perform a check. So I have to justify my actions to him/her, not to the authors.

If, as an author or as a second reviewer, I noticed a very blatant case of citation shopping, I would consider it appropriate to write to the editor privately to suggest investigating. but this has never happened to me up to now. (Although there have been a couple of borderline cases.)

Honestly, unless it's particularly blatant (i.e. five suggested citations all to the same people etc.) I tend to assume people are doing this anyway, or at least extend them the benefit of the doubt.

So my core advice? Spend no more time worrying about this than you already have.

If you really care, the way I would approach this is to phrase your comment as if you had read the paper. So, for example:

"The authors may wish to consider citing the recent article by Fomite et al. Highly Topical Research is Highly Topical in this month's issue of Journal of Our Field. Based on my reading, their findings in Table 2 would strengthen the core argument of this paper."

I think that you should avoid remarks like this. Avoid politics and stay focused on science.

Is this the only paper you refer to in your review? If you have other places where you refer to other papers by other authors, what makes you think they will able to single out the paper you suggest as (falsely) your own?

Instead of the way you suggested to write it, how about something like this:

I suspect that the authors overlooked a very recent paper by XYZ (link doi ref etc). XYZ provide these new data and that interpretation which conflicts with point A of the authors and supports their point B. I think it is important that the authors address these new findings so their paper does not become instantly outdated and keeps at pace with new development in the field.

By phrasing it this way, you are doing the following:

1. You put the focus on the scientific content of the new paper. Instead of saying "here's a new paper, cite it", you point out the scientific reasons that this paper is relevant.
2. You leave the choice of citation to the authors. Again, by not saying "cite it" you lower the chances of them thinking it's yours. If the paper is indeed relevant as you think it is, there is no reason that they do not cite it. It's their paper after all, and if they choose not to cite the paper, it's their call (pending editor's approval).
3. You mention the benefit to the authors by reading and possibly citing the new paper. No one wants to publish stuff that's no longer relevant, or superseded by other studies!

I also think that by framing your comment similar to what I suggested, the question of whether they think you are the author or not becomes unimportant. What's important is the science: the point is to make the authors understand that the paper has scientific importance and should then be cited, and even if they think that you are the author of said paper, they will not think you are forcing them to cite it because you are trying to increase your H-index or whatever.