Maybe the astilbe needs more water. Or is infested by weevils. Both kinds will die down on their own in the fall, no point in cutting them back. And you want to let the foliage go through its natural cycle, which is liable to include transfer of nutrients from the dying leaves to the rootstocks.

Move when you'd like, but it's risky during dry periods to move moisture loving plants. It would be better & easier to wait until the fall rains return. The soil will be looser & the plants won't suffer shock like now.

The dormant state was probably already triggered in the pot from going dry prior to planting, so it's not dying just preserving itself. Astilbe are tough plants. My family thought I was crazy when I purchased dead looking 2 gal pots in August for $1 one year. They emerged in spring as well as other established ones here. Since they're heavy feeders, give them some rabbit manure in October every year & they'll be happy along with water throughout the growing season.

A soil enriched with a lot of compost is also going to help retain the moisture both Thal & Astilbe prefer. Perhaps you can prep that new spot for the Thal now & by fall will be richer soil.

If you modify the soil with amendments you will have to dig the planting up later and re-amend every time these have broken down enough for the soil to re-consolidate etc. And digging in amendments tends to open soils up, make them breathe more. If moisture retention is the goal it is more effective to mulch than amend. Amending of beds is best limited to short-term plantings that are frequently re-done anyway, i.e. flowering annuals and annual vegetables. Longer lived plantings are better made in existing soil, loosened at planting time, and mulched afterward. Where a different soil seems called for that should be brought in and dumped on the ground, made into mounds, berms or raised beds, without digging into the rejected dirt already there. Or if raising the grade in a particular spot would be a problem, then a bed shape should be dug out, the unwanted material taken away, and the replacement soil used to fill the excavated area.