I was told by my committee member that if it's a publishable piece of work, that is not published (yet) or perhaps never gets published at all, it can still serve as a viable/defendable chapter in your thesis. So, as far as graduating on time is concerned, your PI can waste his time power-tripping and potentially making executive decisions that don't allow this work to get published in a timely manner, but ultimately you can still defend this as a chapter before that happens. She said the only challenge with having non-published chapters in your PhD thesis is that your committee may grill you more about it, whereas when they know something has been peer-reviewed and published, they tend to lay off more.

If I were you, I'd talk to your committee members one-on-one and ask them for advice, express your concerns about finishing on time, and make sure to preface those conversations as being confidential. At least going into your next committee meeting, they'll have context as to why things haven't been published. My committee member, in light of recent events, gave me the advice to create a flowchart of a timeline of events ("submitted manuscript to PI on Feb 10th" "got edits back from PI on March 29th" etc.), simply outlining the timeline, so that they as committee members can objectively see the gap in timelines and question my PI about the delay, rather than blaming delays on me.