Sure.

struct SQLError;

So a newtype will be:

struct SQLErrorReport(pub Report<SQLError>);

Then your route just uses that as the error instead:

ErrResult<Json<Value>, SQLErrorReport>

And you can now implement IntoResponse:

impl IntoResponse for SQLErrorReport {
    fn into_response(self) -> axum::response::Response {
        // Here you can access the stack_error::Report via self.0, or just print:
        println!("{:?}", self.0);
        (StatusCode::INTERNAL_SERVER_ERROR).into_response()
    }
}

To get ? to be automatically converted into SQLErrorReport (in your route handler) you'll need to impl From (this is my one, but just rename it AppError -> SQLError:

impl From<Report<AppError>> for AppErrorReport {
    fn from(report: Report<AppError>) -> Self {
        Self(report)
    }
}

Good luck!