Hi,
UpdraftPlus calls upon PclZip (in your case), and PclZip in WordPress is configured to use the root of your WordPress site for its temporary files.
You can change that by defining PCLZIP_TEMPORARY_DIR in your wp-config.php.
e.g. to cause it to use your uploads folder instead (which is usually writable, so a good choice):
define('PCLZIP_TEMPORARY_DIR', ABSPATH.'wp-content/uploads');
If you're using UpdraftPlus on work for clients, then please do take a look at UpdraftPlus Premium - https://updraftplus.com/shop/updraftplus-premium/ - it's only people buying the paid product that makes it possible for us to produce, or provide free support, for the free product, which we want to continue (so that e.g. non-profits like you've used it on can benefit).
Best wishes,
David