Product Owner in Nexus Retrospective
You have three Scrum Teams working on the same product using the Nexus Framework.
According to the Nexus Guide, one part of the Nexus Retrospective is that it "consists of each Scrum Team holding their own Sprint Retrospective as described in the Scrum framework." According to the Scrum Guide "the Sprint Retrospective is an opportunity for the Scrum Team to inspect itself and create a plan for improvements to be enacted during the next Sprint." and "The Scrum Team consists of a Product Owner, the Development Team, and a Scrum Master."
As the Product Owner can, but should better not be divided into three, it is not possible to have "each Scrum Team holding their own Sprint Retrospective". So what should the Product Owner do? Only attend the third part of the Nexus Retrospective, where "appropriate representatives from the Scrum Teams to meet again and agree on how to visualize and track the identified actions"? Attend one Team Retrospective and appoint a deputy for the others? Something totally different?
If the PO has been collaborating as a team member and providing integration assurance through the NIT, then he or she may have a good idea of how much time to spend with each team in their Retrospective.
In a typical gather data => generate insights => decide setting for the team retrospectives, it's a bit hard to have the PO only in for a certain time in each or any of the team retrospectives.
Why is it not possible for the PO to attend 3 Retrospectives. The Nexus guide does not say that all 3 of those Retrospectives have to occur at the exact same time. It just says that they all have to occur. Schedule them consecutive instead of parallel. Keep in mind the time boxes provided in the Scrum Guide for the events as the Nexus guide states
The duration of Nexus events is guided by the length of the corresponding events in the Scrum Guide. They are time-boxes in addition to their corresponding Scrum events.
No one has ever said that Scrum is easy and since Nexus is based on Scrum, who would expect it to be easy? This really would not be any different if a single PO was serving on 2 teams (as a lot of companies actually do) that are not doing Nexus. They still have to find ways to split their time appropriately.