A good dry stack retaining wall is supposed to have a batter - a lean back into the slope. That helps support the weight of the wall and makes it more stable. From your blurry pictures it looks like one of the cap stones by the Japanese Maple may have slid off the top into the bed. Just slide it back in place. The wall looks perfectly fine.

Put another way, each course of stone should be slightly set back 1/4 to 1/2 inch from the course below. That is the batter. A dry stack wall is not supposed to be plumb, perfectly straight up and down.

You usually don't see walls leaning backwards into the soil they are retaining! Pics can be deceiving, but it looks like the upper 5 courses + cap are tilting progressively as you go up. And the face concaving as well starting at the 6th course down looks as if slid backward. Eliminating it was built wrong originally or was pushed in mechanically, I would guess that there is washout of the soil it's retaining or the base it is sitting on. That may have something to do with the stair and it's base too.

You would have to provide much better pics, and overall views, to get better advice.

Thanks for both comments. I tried to get a few better pics from some other angles. It’s hard with the Japanese maple there to get the full picture but wondering if this gives a better idea of what’s happening.

Much better pictures and yes you have a problem. No it can not be fixed with out dismantling and rebuilding both the wood and block walls.

The basic problem is the footing the block wall is sitting on is failing. That footing looks like it is another wood retaining wall. Wood rots. The wall is settling into the void.

Thank you! In the short term, would adding more soil inside the bed help hold the wall up at least til the end of the season?

I am going to go with no. Adding more weight and hydrostatic pressure pushing on a collapsing wall would not be a good idea and only make the demo harder.

Okay. Thanks. What is a reasonable sense of the urgency around doing the demo? Is there an immediate danger?

The critical factor is the condition of the wood retaining wall. If it goes, it will happen when one of the timbers fails.

This is not a DIY project and I would imagine you may want to get several bids. The landscape and construction trades are awash in gubmint bribe check money and booked months if not into next year in advance. It would not hurt to start calling masons and landscape construction companies now. It may be the end of the season before they can get to it.