How does desk review work? When does a paper go to peer review, and what does an "undecided" status mean?

I assume you submitted to a traditional journal. Traditional journals are very opaque today. In the editorial office, which papers they leave sitting on the desk and which they send to reviewers is almost never made public.

In my experience reviewing for traditional journals, good reviewers are a scarce resource, and not every manuscript gets them. The manuscripts that go straight to reviewers after submission are usually of a few kinds.

First, of course, are special manuscripts that the publisher or the editor-in-chief has asked to be handled. Second are those whose authors or institutions are prominent, or whose titles make it obvious that the research is important. Third are studies on hot topics that are not groundbreaking. Last are papers the editors judge will increase the journal's citations; good reviews and meta-analyses belong here.

Other papers usually enter an unclear state, such as "with editor", "pending assignment" or "office review". The journal simply holds them: it has not rejected you, but it has not promised you anything either. It is like a waiting pool; when the journal runs short of manuscripts, it picks a few to send out for review.

As for papers that are reviewed but receive an "undecided" recommendation, I have not seen that in my own reviewing. Editors don't like asking someone to review and getting what amounts to no review, so there are usually four choices: accept as is, accept after minor revision, accept after major revision, and reject.

At high-level journals with low acceptance rates, two reviewers recommending "accept after major revision" usually amounts to a rejection. These journals have so many strong manuscripts that get "accept after minor revision" in the first round. Everyone likes researchers who clearly know what they are doing; their papers are less likely to cause trouble after publication and less likely to contain serious errors. That is the reality from the reviewers' side.

If, after review, you see your manuscript marked "undecided", it may be a feature of that journal's system. Editors usually choose this status when they want to think further or find another reviewer. They may want to accept your paper but find the earlier reviewers too harsh, so they look for someone more favorable. Or they may feel they cannot accept more papers for now and wonder why the reviewers rated it so highly, so they find another reviewer, delay a few months, or look for a chance to reject.

Personally, I think an "undecided" status is still much better than a rejection. It means there is still a chance.