Multipath TCP is a neat trick that allows a single TCP connection (TCP = Transport Control Protocol, a stateless protocol for long running connections) to use multiple physical interfaces. You could do something similar before MTCP using bonding, but this was annoying to set up and usually required application level code to efficiently use the bonded connection. MTCP makes this much simpler from an application level point of view and it can use widely diverse underlying transport layers at the same time (for instance, WiFi, Cellular and wired connections).
TCP is stateful by definition, and that is why it supports robust error correction and reliable streams of data. UDP is its stateless counterpart.
> bonding, ... usually required application level code
No, it doesn't. https://en.wikipedia.org/wiki/Link_aggregation
> underlying transport layers
TCP is in the transport layer! The layers which you name are lower, such as Layer 2 (Data Link)!
MTCP, being in the transport layer, is working at a higher level of abstraction than bonding or link aggregation. There is no need for application-layer support, but it is possible, and easier, with MTCP than with the Layer 2 solutions, because MTCP is in the transport layer. That is why Go was able to activate it, and the POC uses it, because MTCP controls can be exposed at that level.
It's an extension to TCP that, similar to QUIC, allows you to use multiple address/port pairs to transmit data over a single logical stream. Both client/initiator and server/listener have to opt into the extension. This might need to be enabled explicitly by the application[1], which Go apparently does for you, or judging from other posts may be enabled by default systemwide, depending on your platform.
AFAIU, a major user of MPTCP is Apple and the iPhone, and the ubiquity of iPhone clients motivated implementation in and deployment on Linux servers.
[1] https://docs.kernel.org/networking/mptcp.html#sockets-api
Again, the description of this CVE indicates that the vulnerability does not depend on MPTCP. But it is a factor in the proof-of-concept and its likelihood of success.
So if there was any widespread mutual support of MPTCP, it may shrink significantly as network admins deploy mitigations.