Those databases exist, but they're generally not publicly accessible.
There are basically two types of Earth observation data: from agencies (ESA, NASA, JAXA, etc.) and from private companies (Maxar, Satellogic, etc.).
The agencies, being funded with public money, typically make their data freely available, at least to funding countries. However, in my experience, their missions are typically focussed on weather, climate, etc. Their satellites are at high orbits or geostationary and the images are often in spectral bands outside the visible light. Some missions have/had visible light spectral images, but the resolution is not good enough to resolve cities.
Commercial parties have made a business case out of providing high-resolution images in the visible spectrum. Some, such as Satellogic, have swarms of small cubesats in low orbit with high-definition cameras, providing almost streaming data. Of course, companies need to make money and therefore that imagery is provided only to paying customers. Depending on the size, resolution, number of spectral bands, etc. prices can go up to $1000+ per image (from experience, you typically will not find prices on those companies' websites, only "request a quote").
This ESA page provides a nice introduction to what EO data you can expect from which providers. It also provides an (incomplete) list of some of the commercial parties.
In the specific case of Ukraine: Satellogic and Astraea have launched Ukaine Observer, where they provide high-resolution imagery at no cost to qualifying first-aid organisations. Commercial entities with assets in Ukraine may qualify for reduced-cost access. I'm not affiliated with them in any way, so I cannot provide any other details than can be found on the website.