If you're running with the default local installation that XC sets up for a developer machine then all communication runs to the authoring engine role for both the Sitecore Admin tools and the storefront, so the shops instance will never be hit and hence wont generate any logs.
This is because you're only running a single instance of the CMS, acting as both the Content Management and Content Delivery.
Each instance of Sitecore can only be configured to talk to a single endpoint for the commerce engine. If you look in your ShowConfig.aspx page for your CMS instance you will see a section which looks similar to this:
<commerceEngineConfiguration type="Sitecore.Commerce.Engine.Connect.CommerceEngineConfiguration, Sitecore.Commerce.Engine.Connect" patch:source="Sitecore.Commerce.Engine.Connect.config">
<shopsServiceUrl>https://localhost:5000/api/</shopsServiceUrl>
<commerceOpsServiceUrl>https://localhost:5000/commerceops/</commerceOpsServiceUrl>
<commerceRequestTimeout>120</commerceRequestTimeout>
<enforceSsl>true</enforceSsl>
<defaultEnvironment>HabitatAuthoring</defaultEnvironment>
<defaultShopName>CommerceEngineDefaultStorefront</defaultShopName>
<defaultShopCurrency>USD</defaultShopCurrency>
<certificateThumbprint>THUMBPRINT</certificateThumbprint>
...
</commerceEngineConfiguration>
You can see above this is set by default to communicate to the engine listening on port 5000 which is the authoring instance.
In production you would have more than once instance of the CMS, your content deliverymanagement instances would have this configuration pointing to your Authoring Engine endpoint as above, and the Content Delivery instances would be pointing to your Shops endpoint instead.
In other words, your shops instance isn't receiving any traffic, which is why it isn't generating any logs.