I made use of publicly available data from the Directorate General of Health Services to get a picture
Data Source: http://facilityregistry.dghs.gov.bd
Distribution Across Divisions
Bangladesh has a Divisional Government systems that splits the country into 7 Divisions. Dhaka hosts the capital, and Chittagong hosts the primary sea port.

Dhaka has the most healthcare facilities among all the divisions in numbers, and Sylhet has the least. However, the data does not properly reflect facility per capita as the population or area has not been considered.
Source of Power/Electricity

(About half of the entries were NULL, treat this metric with caution)
A significant chunk of the reported hospitals are connected to the National Grid. Solar Power has an interesting number of users.

Unfortunately, a good chunk of Healthcare services have no access to power. No Grid connectivity, Solar power or even Generators.

There is a lot more to the story. Visit Data Studio to see more interesting insights!