I haven't looked at DWARF for ages. Can it describe the situation that a variable is valid (in some register) in the beginning of a function, but then goes "out of scope " in the middle of the function?

Yes, with DW_OP_entry_value used in location expressions to indicate that the variable value is in a certain location on entry to the function. However -- debuggers typically don't store all register values on entry to all functions, so usually the stack frame up needs to be instrumented with call site information indicating where the debugger can find longer-term stored copies of the arguments.

In TFA you can see that happening correctly wherever there's a "@entry" annotation from gdb for an argument, in some cases there isn't a longer-term copy of the value further up the stack, in which case the variable remains optimised out.