The typical compiled SDK size is ~4.5kB of flash and 1kB of RAM. It is highly configurable so that it can work in more constrained environments.
Memfault is very efficient in terms of volatile and non-volatile storage requirements. The amount of data collected and stored by the SDK is completely configurable by the implementor.
Metrics and Trace Events are 10's of bytes. The size of a coredump is based on how much memory the implementor wants to capture and can range from a few hundred bytes up to roughly the size of your memory space. The larger the amount of memory captured, the finer grained analysis Memfault can provide.
To learn more about the Memfault MCU Firmware SDK, check out the documentation.