Having worked like this, with a single team working on multiple projects at the same time, on multiple occasions, I have identified numerous reasons to not do this and exactly none at all to work like this.
Ultimately, it will strain or fracture the team, drain motivation, reduce productivity and leave you with two failed projects.
Various companies tried doing this in various different ways, but not of them really worked out in the end.
We tried tackling problems from two backlogs with the whole team. The main downsides there were constantly switching between context, which caused huge overhead, and the inevitable fights with the PO over which project's stories needed to be dropped when we wouldn't make the sprint. Doing one project first and the second after made the fights worse in intensity; doing a story from each in turn made them more common as the overhead reduced velocity.
We also tried assigning some people to work primarily on one project, some people on the other, and some shared, with the idea that both sides would help out if one or the other project would slip. This one fractured the whole team in weeks, with each side just working on a single project and not really caring about the other anymore, losing track of the domain expertise and progress needed for the other project and then just getting annoyed about having to join on meeting for a project they weren't a part of. The team basically ended up being split in two teams, one for each project, but that caused a lot of pain and lost productivity.
Then also we tried working on one project for a sprint, then the other project for a sprint, etc. This worked somewhat. It has less of the issues of the first approach because each project is in a clear timebox, but it will cost you a lot of flexibility when something important happens on Project A but you've just started a sprint for Project B, and then you end up with the same priority fight.
My best advice: don't do it. One person, one team, one project, one goal. Anything other than that is going to cost you tons of morale and productivity, for no gain. Obligatory reading.
Also, as a final note, ask yourself why you want to do this. There is literally no reason to ever consider this; you can just do both projects in series. Complete project A and then complete B once A is done; if you could successfully complete both in parallel then you will always be able to complete them faster in series. Any reasons for starting both at once, are likely rooted in already admitting to yourself that you're going to fail at both projects anyway, and are trying to mitigate the damages by having something to show at the deadline to convince people you need more time/money without them pulling out. Invest your time fixing that problem and leave your people to focus on one thing at a time, that's how they'll work best.