drivers: modem: cmd_handler: split cmd_handler_process() implementation

cmd_handler_process() does two major things:

 - reads data from modem interface and fills data->rx_buf,
 - processes data in data->rx_buf.

Split implementation accordingly to two separate functions, which
improves readability (less automatic variables to follow at once) and
simplifies refactoring of each action.

No functional change was intended in this commit.

Signed-off-by: Marcin Niestroj <m.niestroj@grinn-global.com>