I do not feel like risking it with OSM, unless it is possible to get permission from them first. Having a proxy server would have some downsides, in case the app gets a lot of users around the world it would require redundancy and several servers to reduce latency, which also comes with a cost.

Mapbox seems to have reasonable pricing. Is it Raster Tiles API for the satellite preset?

Unfortunately, it is impossible to make some kind of documentation for each provider, because each provider has its own characteristics and pitfalls, which you can only learn about from the official license agreement.
In addition, Online Maps has presets for many providers, and all of them occasionally update their license agreements. This means that such documentation will always be out of date, since I don't have enough time to keep track of every change.

To be honest, I have not heard of anyone having problems with OSM.
But if you are worried about this, you can easily take the load off OSM servers by passing requests through your own proxy server with cache.

Personally, I like Mapbox.
I just checked and it changed the prices again and at the moment you need Static Tiles API or Raster Tiles API.

I work for a very small and newly founded company and we plan to release a paid app on Google Play and App Store that is using Online Maps with tiles in one of the features.

I've read the "Licenses and API keys" in the Readme file, which states that the presets for all map types are provided for testing purposes. That sums up my current situation, I'm looking for a provider that is either free for our use case or cheap enough to be worth it.

We were originally going for OpenStreetMap but according to their requirements our use case is forbidden: "Heavy use (e.g. distributing an app that uses tiles from openstreetmap.org) is forbidden without prior permission from the Operations Working Group." Hosting our own OSM server is probably not an option because of the cost.

I've looked at Google Maps Tile API but some sources say that the API is deprecated and can no longer be licensed. On Google's page it also states: "The Tile API is available only to select partners, and is not included with the Google Maps Core Services". Which probably means the chances are slim to be able to use Google as a provider.

There are some providers I can select in Unity that do not have any extra fields or keys in the Key Manager. (ArcGIS, CartoDB for example) What about them, what do I need to do in order to license the usage of those, since I cannot find where to add a license key or user information?

I've also looked at Mapbox that seems to be quite cheap, but it is a bit unclear what type of license I need for the usage Online Maps provide.

Is there any in depth documentation for each provider? I want to know what details each provider usually require and where to get the correct license.

Any recommendation on what provider that would be most suitable for a small company with limited economical muscles currently?