How to log all rest api calls in magento2?

[This may not be a good way to log the Rest API]

We should try with Plugin - Magento\Webapi\Controller\Rest::dispatch():

app/code/Vendor/WebApiLog/etc/frontend/di.xml

<?xml version="1.0"?>

<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
        xsi:noNamespaceSchemaLocation="urn:magento:framework:ObjectManager/etc/config.xsd">
    <type name="Magento\Webapi\Controller\Rest">
        <plugin name="rest-api-log"
                type="Vendor\WebApiLog\Model\Plugin\RestApiLog"/>
    </type>
</config>

app/code/Vendor/WebApiLog/Model/Plugin/RestApiLog.php

<?php

namespace Vendor\WebApiLog\Model\Plugin;

class RestApiLog
{
    public function beforeDispatch(
        \Magento\Webapi\Controller\Rest $subject,
        \Magento\Framework\App\RequestInterface $request
    )
    {
        $request->getModuleName();
        $request->getActionName();
        $request->getPathInfo();

    }
}

You can use the following FOSS module:

https://github.com/vladflonta/magento2-webapi-log