Can the sample libraries that come with Dorico be used in other applications?

Can the sample libraries that come with Dorico be used in other applications? If so, as what format? Is it intuitive to set up?

Any application that supports VSTs (or Apple’s Audio Units) can use them. They shouldn’t need any setup in most apps, though obviously you’ll need to read the documentation for that app.

To be a bit more specific: The sound libraries just contain the sound data, but it needs a “player”, i.e. a VSTinstrument plug-in that can play and reproduce the sounds. In case of Dorico (or the Steinberg sound libraries) HALion Sonic SE is that VSTinstrument. If you get HALion Sonic SE working in another host, then you can also use all the sound libraries of Dorico as well.
HALion Sonic SE adheres to the VST3 standard, so any host that is compliant to VST3 shall be able to load it.

If you have Dorico installed, and his eLisencer keys in place, then yes. You should get access to HALion SE as a plugin in other hosts, and/or as a stand alone executable player (which also includes a nice built in MIDI player/recorder). The Dorico key can also unlock the following HALion libraries (they ship with Dorico):
HALion Sonic SE Basic
HALion SE Artist
HALion Sonic SE Pro
HALion Symphonic Orchestra
Olympus Choir Micro

I usually recommend grabbing the independent SE installer and running it first if one intends to use HALion SE in alternate hosts. It checks to make sure everything is at the latest version, and provides options to make sure you have all the plugin types you’ll require (VST2, VST3, AU, AAX), and that they are located in one of the more standard system locations for sharable plugins.
https://www.steinberg.net/en/landing_pages/halion_sonic_se_3/halion_sonic_se_free.html

This link offers a free key. This is optional if the system already has a Dorico/Cubase/Nuendo key. It does NOT unlock any HALion content that isn’t specifically prepared to work with the free player.

Note, this does NOT include the effect plugins that can be plugged into Dorico’s mixer inserts such as REverence. Don’t expect to find those in your third party DAW. Such plugin collections can also be a bit different from one Steinberg host to another.

Thank you all for your great, detailed feedback. I love this forum!