Is it ever acceptable to run a project that is maintaining multiple backlogs? The answer is simply, no, it’s not acceptable, and you should see it as an impediment. The reason being, if a separate backlog is created for things like tech debt and bugs, or even a different part of the project’s functionality, each of these additional backlogs will have their own ‘top’ priority. So, how can you be sure which ‘top priority’ really is TOP PRIORITY?
As a Scrum Master, you can facilitate the necessary meetings to agree on how the issue can be addressed. It may take some time to do this, as there may be some conflict around which PO or stakeholder’s backlog item is ranked highest once the backlogs are consolidated, but as long as Business Value and Return on Investment play a rational part in these discussions, the outcome should be that you have one prioritised backlog that all your teams are working from.