I bought two Sedum "boogie woogie" yellow flowered groundcovers, planted them close to each other in the same soil and have been watering them equally, but one was decimated over the course of a month after planting. It has now been in this sad-looking state for about two months, no better, no worse. The other one seems to be thriving, no issues.

I've noticed small milkweed bugs (Lygaeus kalmii) around the plant on a couple occasions, but otherwise no obvious sign of pests - those aren't supposed to really damage plants right?

I've attached pictures below, one picture of the healthy plant with several pictures of the diseased-looking one. Also included a picture of bubble-looking things in the soil but assuming this is osmocote/slow release fertilizer?

Any ideas on what might be going on - Is there any particular condition that makes sense here? Should I leave the plant in the hope that it will come back strong next year or instead dig it up?

Yes to the osmocote.
It looks like a root problem. Some nurseries over water. The plants either get used to that daily watering routine, they need it because they are root bound or they rot the roots from being constantly soaking wet. One sign that this is going on is if the inside of the plant near the crown has a lot of dead, black, hanging leaves. The top of the plant may still look good or salvageable.
What I do in this case is dig it up and separate the good from the bad. If the stems still look ok, you may get it to bud up so leave that if the root is good.
So it appears that you do have some buds coming back so that is good. Part of the plant should recover. You may end up with a few smaller plants.