Migrates the 'stepIn' request handler to have well structured types
instead of raw json values.
I also noticed in the 'next' request handler we were not passing the
'RunMode' flag. Updated the 'next' request handler as well.
Replace Get{Signed,Unsigned} with GetInteger<T> and return std::optional
so you can distinguish between the value not being present and it being
explicitly set to the previous fail_value. All existing uses are
replaced by calling value_or(fail_value).
Continuation of #129818
Return a std::optional<bool> from GetBoolean so you can distinguish
between the value not being present and it being explicitly set to true
or false. All existing uses are replaced by calling
`value_or(fail_value`).
Motivated by #129753
