This PR was spun off #904 for clarity.

Because the adoption of a linalg_state_type was successful and flexible enough, it is proposed to extend the linear algebra error handling type by introducing a new state_type base class as part of the stdlib_error module.

This would provide a unified framework for managing error states across all different modules of stdlib, not only linear algebra but also I/O, filesystem and other modules.

The state_type class has the same contents as linalg_state_type: integer error flag, fixed-size character storage for messages and error locations, and type-bound procedures for error checking and reporting. The existing linalg_state_type now extends state_type, ensuring consistency - and interoperability.

The linear algebra modules still require type(linalg_state_type) outputs. We could make them class(state_type), optional, intent(out), so they would seamlessly handle both derived types. However, in Fortran, polymorphic arguments cannot appear in pure procedures, so another alternative would be to template them with fypp.

relevant discussion: #224 #212 #95 #219

cc: @jvdp1 @jalvesz @fortran-lang/stdlib