Alumroot / Coral Bells (Heuchera) plants unfortunately have a reputation for being sensitive to being planted too deep, over-mulched, or over-watered. They are often found in very sharply-drained habitats in the wild, where moisture is not excessive and the soil not very compacted. They tend to tolerate moderate drought better than heavy or wet soils. When watering, checking the soil moisture rather than relying on a set schedule is best to avoid under- or over-watering. Feel the soil about five inches deep, and water well only once the soil has become somewhat dry to the touch at that depth. If damp when checked, most plants (including Heuchera) will be fine if watering is withheld until the soil dries more.

Make sure mulch isn't touching the crown (where stems emerge from the roots at the soil surface), keeping it away several inches on all sides for better airflow. While it might be early yet for common crown-rotting infections like Southern Blight, those conditions can predispose plants to infection.

Wilted plants that do not recover when the root zone is damp likely have contracted root rot and would need replacement, since they rarely if ever recover. If you want to inspect the roots, look for those with a mushy outer layer that detach easily and leave behind a stringy inner core -- these are characteristic for root rot pathogens. To be fair, these fungus-like organisms are fairly ubiquitous in the environment, so eradication is not possible or practical to attempt, but they only tend to attack plants that are already under stress from having roots stay too wet. Roots that are either still alive or which died from other causes tend to take more force to break, and they'll usually snap cleanly in half in comparison.

If you replant with replacements, keep the rhizome (the horizontal thick stem that the Heuchera leaves and roots attach to) just at the soil surface; don't bury it under soil or mulch. Some Heuchera plants almost develop a "neck" over time as this rhizome gets longer with accumulated growth, because it remains exposed and not covered in soil/mulch.

The rusty-brown patches of dead leaf tissue do not look like an infection responsible for this type of dieback. If an infection at all (it could just be scorch from dying roots being unable to keep the leaves hydrated, which is why they wilt), it's minor and those individual leaves could just be snipped off, were the plant otherwise healthy.

Heuchera can tolerate lots of direct sun, but prefers a semi-shaded exposure, based on where they grow in the wild. If the site isn't full sun once the nearby trees leaf-out, you can try growing Heuchera there again, but if it's still very hot and sunny during the summer, another species might fare better (including if the soil skews damp in that area due to drainage patterns).

It's possible some type of crown rot, behaving similarly to Southern Blight, is present in this portion of the planting, but unfortunately in that case there is no intervention that can cure plants afflicted with that disease. Plant vulnerability to such infections increases in wet conditions or where air circulation is poor, though some species are more susceptible than others. Fungicides are preventative measures only, so avoiding plant vulnerability by having the site conditions meet their needs as much as possible is generally the best preventative approach. Maybe, being towards the base of the hill you mentioned, the Heuchera are staying a bit wetter (or compaction from anyone that might step off of the sidewalk onto that soil is impacting drainage). We've seen Heuchera villosa occasionally die back even in containers with what appears to be good drainage, though, so sometimes they just might be very fickle about planting depth and soil moisture level. Its relative that is more common in Maryland, Heuchera americana, tends to grow in rock crevices and similar habitats, in sites like open woodlands along the Potomac River (well above the water line); this can be seen in some of the photos in the linked page, which suggests they prefer to be on the drier side.

Miri

You're welcome.

You should be able to transplant them now; just keep an eye on their watering needs as they re-establish roots in their new location.

Miri