Your question raises several quite serious ethical questions - thank you for posting it!

From the last part of your question it looks to me that you actually do have a conflict of interest, since you are afraid that what you write in your review may impact your future relations with this research group. I think it is best for you to withdraw from reviewing this manuscript, and fully explain your decision to the editors. I would even consider sending them a draft of your manuscript, if this does not violate your arrangements with other authors.

I am not sure your own paper can not be published. In my area it is not uncommon for two groups to produce similar results almost simultaneously (the second paper is submitted before the first is printed). This does bring some hard discussions sometimes, especially if the ideas are published on arXiv or presented at conferences. However, this does not stop papers from being published. Of course, you should not use anything from paper B to improve your paper A.

To summarise: In my opinion, it's best for you not to study paper B in too much details, withdraw from reviewing it, explain this decision to Editors, and continue working on your paper A.

I will address the part of your question concerning whether it is okay to tell your collaborators about paper B, which was not discussed in Dmitry Savostyanov's otherwise excellent answer (with whose content I agree 100%).

Let me start with a general remark: from an ethical point of view, when one agrees to keep some information confidential before seeing that information, it seems to me that such agreement is inherently limited in its scope rather than absolute. As a (rather extreme) example, say a friend is offering to tell you a secret but asks you to promise to keep it in confidence. You agree, and he then tells you that he murdered 10 people in cold blood. Obviously the usual assumption that it is your ethical duty to keep your promise is no longer valid at that point (except perhaps if you are his lawyer or priest, and even then maybe not).

The point of the above extreme example is that the context of the confidentiality promise, of the information you have promised (based on only partial knowledge of the nature of that information) to keep secret and of how that information interacts with your own work and other ethical duties to other parties, matters. In the current situation, I would argue that the situation is unusual enough that it is not covered by the usual default rules about the confidentiality promise being a very strong and essentially inviolable one. You are in possession of information that is highly significant to your coauthors, to whom you have some ethical responsibilities, but also a duty to respect the confidentiality of the author of paper B to the extent possible. How to resolve that tension?

My answer would be that it is okay to tell your coauthors about paper B. Don't go into any details, and in fact as Dmitry suggested, don't even study paper B in detail yourself to avoid implicating yourself in a very clear conflict of interest and possible conflict with your own conscience. But it is not unreasonable to caution your coauthors about the situation and discuss with them how your joint project should proceed in a way that does not needlessly cause a large waste of your combined efforts. At least, if you proceed in such a way then I think a reasonable person would not judge you harshly for what is in my view a small (and make sure to keep it as absolutely small as possible) violation of the confidentiality principle that is done in order to serve a greater good and satisfy your ethical obligations to other parties affected by the information.

A very good question indeed: a lot of us can face a similar dilemma.

I believe peer review is almost always about conflict of interest. [EDIT] As discussed in comments below, this assertion seems exaggerated. However, pure open research might be rare. There are many fields where universal principles cannot be found, and discussed only at the level of truth. Incremental improvements are common. Grant funded research is competitive, and its evaluation leads to biases. To summarize it in a saying that exists in different forms:

to steal ideas from one person is plagiarism; to steal from many is research

Who is the original author? Wilson Mizner? Steven Wright? Joseph Cummings Chase? Asa George Baker? Is this quote a cut-and-paste from many? Sources are discussed in Quote investigator: If You Steal From One Author, It’s Plagiarism; If You Steal From Many, It’s Research

Because to be asked for a review of a paper, you need to share a similar interest (unless the system is flawed: how many have been asked for reviews outside their area of expertise?). And in the academic world, working on a similar topic cannot often be done without biases. And some apparently act unethically. I learned about Paper A submitted in a conference in Country C, rejected, and a year later same conference (ICIP 2003, Barcelona) at the, people for country C (in fact, one was in the technical committee of the conference) presented a quite similar Paper B, just aside to the guy presenting the resubmitted and now accepted Paper A. No proof.

In 1991, two groups, independently, published a paper on a very similar topic (chirplets). Paper A was published first, but Paper B was submitted first. Endless discussions followed.

If you withdraw your expertise, a clean and honest move, Paper B will follow its path to the reviewing system, independently of you. And quite fairly. Then, you can invite your coauthors to hurry, because you have heard that "a similar paper" was submitted. Or say them you have been asked to review it, and refused. And submit it to another journal. Hoping yours will make its way faster that the other, because better written, because of a fast editor, of a lucky hand of gentle reviewers. Perhaps, you can bet on a different field of application.

And as suggested by @Ian in a comment, why not openarchive (arxiv) your preprint, to set a date?

Whatever your choice, it would be difficult to act now as if you never received this paper to review.

When faced with the dilemma of independently duplicated work and peer-review confidentiality, it is essential to uphold academic integrity and transparency. You have correctly identified the conflict of interest in reviewing Paper B and have taken the appropriate step by informing the editor. This allows them to decide whether your review can remain impartial. Peer-review confidentiality is a cornerstone of the publication process, and it is critical that you do not share Paper B with your co-authors for Paper A. Even mentioning the existence of Paper B or its content could introduce bias or compromise the integrity of your review. However, you can still proceed ethically with Paper A by acknowledging the potential overlap in your submission. When submitting Paper A, include a detailed "Competing Interests" or "Conflict of Interest" statement to the target journal. Explain that you are aware of independent research addressing similar work and that you have recused yourself from reviewing related submissions to maintain objectivity. Additionally, consider reaching out to the authors of Paper B to establish contact. This demonstrates academic courtesy and may help coordinate your submissions to avoid duplication. If both papers are submitted independently, the journal handling Paper B will likely assess the overlap during its review. Your responsibility is to ensure your own work is accurate, transparent, and compliant with ethical guidelines. By disclosing your awareness of Paper B and recusing yourself from its review, you uphold the principles of fairness and integrity in the peer-review process. Ultimately, the decision to proceed with Paper A rests with the editor, who will evaluate the relevance and novelty of your work in light of Paper B’s existence. By acting transparently and ethically, you fulfill your obligations as a researcher and reviewer.