Peer-review -- Can I ask to cite my already published paper that is relevant? I have to review a paper for a journal that is on some work related to a paper I published 2-3 years ago.
The authors do not cite and compare our work although they try to solve the same problem.
In particular they use a similar fairly innovative way for the field to treat the input data, as we and another publication did, but they cite neither of these 2 papers.
Is it an issue of conflict of interest if I ask at least for a citation of these two papers that are preexisting (and one of which is mine), and ask also for a performance comparison with at least one of the competing methods?
If you are absolutely certain that you know (say) two papers which are clearly relevant for their work, you should state it:

The authors should comment on the work presented in [1, 2] and how their work improves on that or is different.

Add more details if you want to be helpful to the authors; for example, if the work [1, 2] uses a very different methodology than the present paper, you may want to offer a bit more detail to help the authors out. But it is voluntary. Also, whatever you write might end up copy-pasted in the final paper.
If you are not absolutely sure the papers are the most relevant and would improve the paper, you might still write:

The authors may want to comment the related work [1, 2].

maybe with more qualifications or detail. You can certainly make friendly suggestions, but given the power relations in play, you should explicitly mark them as voluntary improvements or such.
Also consider that there might be a lot of related literature that would be as appropriate to discuss as yours and the authors had to cut off their literature review at some point. In such a case, asking them to cite your paper in particular seems suspect. You should adjust the certainty of your recommendations according to how well you know the field.