debug_print_backtrace() to String for log-file

Use another function. debug_backtrace() returns an array that you can loop through, format and save:

$data = debug_backtrace();

Or use output buffering for the formatted output string:

ob_start();
debug_print_backtrace();
$data = ob_get_clean();

It's possible to do it with even less code, actually. Avoid the overhead of buffering with...

$error_string = (new Exception)->getTraceAsString();

That gives you the exact same output as debug_print_backtrace() stored to the $error_string variable.

And if you want to get more information for a more valuable stacktrace (line numbers, local object vars, etc.), try...

$error_string = print_r($e->getTrace(), true);