For everyone who is confused by what is going on, here's the explanation:
Today, there are 2.5 Mono's:
Mono that lives in https://github.com/mono/mono. This is the original Mono codebase that was written back then and was the .NET Framework for Linux, with corresponding compat. and such, pioneered by Miguel De Icaza, who now seems to be happier in Swift land. At the present day, it was receiving very little maintenance and I don't believe was actively used. Please correct me if I'm wrong.
Mono that lives in https://github.com/dotnet/runtime/tree/main/src/mono. This is the Mono that got merged into .NET, becoming the building block for multiple components and one of the official runtime flavours. It is actively maintained and is at relative feature parity with CoreCLR, predominantly serving mobile targets (iOS, Android) and WASM as well as exotic or legacy targets like ARMv6, LA64, s390x(?), ppc64. It is also useful for initial stages of new platform bring-up process. Note that you are not expected to use it for targets that support CoreCLR due to a massive rift in performance between the two. When you are using it, you do so as a part of standard .NET toolchain - it is picked automatically for appropriate targets, or can be opted into with some configuration.
Mono that lives in https://gitlab.winehq.org/wine-mono/mono which is a Mono fork actively maintained by Wine for its own usage. Going forward, any possible ambiguities regarding ownership and stewardship are considered resolved and the ownership of mono/mono and everything related to it is transferred to WineHQ.
Honorable mention also goes to private Mono fork used by Unity which they are (painfully) trying to migrate from.