If you want to change the header logo only on the checkout page using XML, then follow the below instructions:

First, you should override the checkout_index_index.xml file in your theme and add the below code between the body.

<referenceBlock name="logo">
<arguments>
<argument name="logo_src" xsi:type="helper" helper="MagemonkeyCustomModHelperData::getLogo"></argument>
</arguments>
</referenceBlock>

Then, you need to create a helper or add the below function in your exiting helper file. (here I have created a new helper file in my module)

<?php
namespace MagemonkeyCustomModHelper;
class Data extends MagentoFrameworkAppHelperAbstractHelper
{
protected $_request;
public function __construct
(
MagentoFrameworkAppRequestHttp $request,
MagentoFrameworkViewAssetRepository $assetRepo
) {
$this->_request = $request;
$this->_assetRepo = $assetRepo;
}
public function getLogo()
{ 
return $this->_assetRepo->getUrl('images/checkout-logo.png');
}
}

*Note: I have tried this code in Magento 2.4.2