Finding "shared goals" in moments like this can be really helpful. Then when you meet with your new manager, you can explain the state of the union in a factual way that puts you and them on the same team. That might sound something like:

"Hey BOSS. I've been looking forward to this time today, thanks for meeting with me. I know we've got a lot going on, so I wanted to dive right in.

Here's a high level view of what I'm focused on right now. (SHARE DETAILS)
I also know that with (Former Boss)'s departure, projects X, Y and Z now also need to get taken care of.

I would love to talk through which of all these projects are the most important to handle right away, and come up with a game plan to get the rest of these done well and on time. I'm not sure if you're planning on hiring a backfill for (Former Boss) or if you have another plan for this work/team, but I'd love to help however I can in getting things back on track."

Finding a common/shared goal (getting things done well and on time) makes you stand out (vs. someone who just says "I can't do this all by myself.") That said, you can't fully control the situation, so if you're getting the spidey-sense that things might get worse before they get better, you can decide whether or not you also want to start looking for other opportunities.