Disclaimer: I am not an expert and have never owned a rain frog. All statements made are the result of (extensive) online research. Sources may be found at the end of this comment (Assuming I remember)
Additional disclaimer: All research was originally done on the Common or Bushveld rain frog (Breviceps adspersus) or rain frogs as a whole. Breviceps poweri seems to have a similar range and is still part of the same genus so this should be somewhat helpful. Please do your own research to verify any claims made.
Final disclaimer: There is a lot of contrasting or false information about these animals so I was forced to evaluate the likelihood of various claims. I may have been wrong.
Without further ado, here are my findings;
1. Chytrid testing
Unfortunately, as an amphibian, these frogs are vulnerable to Chytrid fungus, which can be and is fatal. Before introducing tankmates, it is important to use a test kit, available online, on all frogs to avoid transferring this fungus and killing the frogs.
Important: Quarantine your frogs separately until test results return as the associated disease can be passed through contact or even water.
Chytrid is treatable, as the fungus is especially vulnerable above 32c. Treatment at higher temperatures for an extended period (5+ days at 32c, ~16hr at 37, etc) have proven to be effective, though these should be attempted with care (Do not microwave a frog).
Chytrid kills quickly so getting a test is a matter or urgency, assuming this is a wild caught frog (I haven't heard of any successful breeding of any Breviceps in captivity but please feel free to correct me as that would be wonderful news).
2. Substrate
Breviceps is a fossorial genus that avoids predators by digging into the ground around them. In this image, the tank sediment seems to be relatively shallow and coarse. I would suggest a different sediment, more closely mimicking their home territory of Zambia. This should be sandy and to a depth of at least 15 to 30 cm.
Also, despite their appearance, these sands are often mineral rich (at least the (very similar) velds of B. adspersus are) so choosing a sediment that boasts good mineral contents is advised.
3. Rain
Breviceps are unable to jump or swim, due to their ridiculous stature, and (conjecture) are therefore forced to the surface by heavy rain. This is also when they feed and mate, as it signals the arrival of the plentiful rainy season in their native Africa. To mate, and likely this represents a broad prefered humidity, Breviceps require 50 to 80% humidity, so this should be replicated in 'summer'.
To simulate the heavy rain, every few months (Or maybe once a month, or maybe longer; research was inconclusive), heavy misting should be done. This should draw the frog from its burrow, where it will begin to hunt. Breviceps hunt in the dark and are easily threatened so this may need to be done without lights or human presence. See also; feeding.
4. Feeding
As aforementioned, these frogs likely only feed after rains and in dark conditions when they feel safe to. Any 'puffing up' is a threat response and decreases the likelihood of a successful feed. The frogs should be given an ample supply of live (Dead prey seems to put them off it) ants, termites, and/or arthropods. In captivity, these frogs seem to be fussy eaters so an array of feeder species may have to be tried.
Important: My research seems to indicate that most pet Breviceps are fed too frequently which disrupts their natural balance, a factor I believe plays a role in their failure to breed the genus. However, this is not a conclusive opinion and, if the frog appears weak or frail, earlier feeding is obviously advised.
Important: Do NOT use wild caught prey as these can carry pathogens that may harm the frog.
5. Winters
Breviceps (Or at least B. adspersus) spent the dry winters deep around natural supports such as tree roots, stumps, logs, or rocks so these should be provided for both shelter and better architecture.
6. Enclosure refinement
Breviceps actually wander up to 2m away from their burrows during the mating season to hunt or advertise their availability for a mate (and further when they find a suitable partner), so a larger tank, only if affordable, might be good. This is not an incredibly important element but might improve quality of life(?).
Additionally, in their home savannahs, leaf litter can be found on the ground. To provide shelter and reduce stress while feeding behaviour occurs, a sparse cover of leaf litter around the tank could be provided. This should be replaced semi-regularly to avoid mold which is never a good decor choice.
7. Handling
This is a wild animal, and not a social one at that. As such, intensive handling should be avoided. However, in the course of caring for the frog, handling may sometimes be required as in the Chytrid test process or while cleaning the tank. This causes high stress for the frog and may result in it inflating and screaming, as it does not know what is best for it.
When handling is required, it should always follow these guidelines as a minimum;
Follow up
B. poweri is an understudied species, like all Breviceps, so a comprehensive care guide is impossible. While I hope this addresses most initial concerns, I cannot possibly hope to cover all questions involved in owning an animal, especially as a new owner.
Please feel free to contact me either on this comment or by PM through Reddit and I will happily help to answer any additional questions, at any point.
Best of luck with your new frog and remember that I am here to help, if needed.
Sources (Can't believe I remembered this after writing all that!):
https://archive.org/details/animal00davi/page/456/mode/1up
https://en.wikipedia.org/wiki/Breviceps_adspersus
https://amphibiansoftheworld.amnh.org/Amphibia/Anura/Brevicipitidae/Breviceps/Breviceps-adspersus
https://en.wikipedia.org/wiki/Brevicipitidae
https://conny123.pixnet.net/blog/post/117053756 (Not very relevant, but I looked at it)
https://www.reddit.com/r/frogs/comments/14ubas3/the_desert_rain_frog_please_ease_my_mind/ (Again, totally unhelpful)
https://www.worldwildlife.org/magazine/issues/fall-2023/articles/meet-the-black-rain-frog-a-grumpy-looking-amphibian#:~:text=Unlike%20most%20frog%20species%2C%20these,as%20tiny%2C%20fully%20formed%20froglets (Sorry for text highlighting)
https://en.wikipedia.org/wiki/Bushveld
http://frogmap.adu.org.za/Species_text.php?sp=160
http://blogs.thatpetplace.com/thatreptileblog/2010/07/12/constructing-a-rain-chamber-the-ultimate-amphibian-breeding-technique/ (For instruction of rain chamber!)
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7976225/ (Hope this isn't a dead link given the .gov stuff)
https://www.amphibianark.org/wp-content/uploads/2018/07/Guidelines-for-minimising-disease-risks-with-captive-breeding....Australian-Frogs.pdf
https://pubmed.ncbi.nlm.nih.gov/21782566/ (Same for this .gov; May require archive.org, though it seems fine RN?)
https://en.wikipedia.org/wiki/Batrachochytrium_dendrobatidis
https://en.wikipedia.org/wiki/Amplexus
https://blog.londolozi.com/2020/02/11/how-much-do-you-know-about-a-bushveld-rain-frog/ (The solvent point isn't true)
https://www.inaturalist.org/taxa/25001-Breviceps-adspersus
https://www.sanbi.org/animal-of-the-week/cape-rain-frog/ (He goes by many names)
https://en.wikipedia.org/wiki/Breviceps_poweri
https://link.springer.com/chapter/10.1007/978-3-031-18923-4_15 (Haven't had time to fully read this)
https://www.conservationevidence.com/actions/770
https://www.youtube.com/watch?v=wa6_c2WJ5iY (Use as a reference for Chytrid testing pose)