This entry will try to point out typical misconceptions about all settings related to the Windows Store using Intune. Please note that it is specifically aimed at Intune using CSPs, which in this case requires a Windows Enterprise/Education license for most settings shown here (verify by visiting the CSP documentation linked here). The behavior using different methods of configuration should be similar, but is not guaranteed.
There are two methods available to achieve this. Currently, both methods provide the same outcome, with the exception of WinGet availabiltiy. Microsoft usually points at the second method described here
There is only one setting required to block access to the store and it is called "Require private store only". Keep in mind that if the store is disabled for a long time, app updates will happen at this point. Consider configuring delivery optimization to avoid network congestion.
This setting can be applied to the user or to a device:
Two settings are required to block the store while still allowing built-in applications to be updated.
The ability to use WinGet (aka App Installer) to install applications is also removed by using RemoveWindowsStore.
In both cases, the user experience when launching the store looks like this:

Unless you have very specific requirements, you should not configure the following settings because they will prevent automatic Store updates. As of May 2023, the only automatic offline update feature available through Microsoft using Configuration Manager is disabled, after being deprecated since November 2021. In other words, updates to built-in applications will be done automatically online or using Winget (via scripts). Manual deployment is possible through using the download command from WinGet
While there are other settings like "Turn off Automatic Download of updates on Win8 machines", only settings that apply to supported Windows 10 an higher will be discussed here. You shouldn't configure settings that don't apply to your operating system, as this could have unintended consequences.
Both methods described earlier will update apps on their own schedule. As of January 2024 there is no reliable way to trigger store updates when the store access is disabled.
DisableStoreOriginatedApps
This not only turns off apps (yes, all of them), it also prevents those apps from receiving store updates. As a reminder, depending on your scenario, you may still need to update these apps for security reasons.
This settings was commonly set to seemingly only allow updates from a defined WSUS server (it's also only in effect while one is configured). In reality it prevents store udpates and prevents subscription activation amongst others
If you set one of the following settings, you might encounter unexpected behavior. Verify that if you want to allow the above described scenario (Block user access | Allow store updates) these should not be configured.
This setting, as Rudy points out, does not disable access to the store, but rather the option to point to the store for unknown file types. It does not prevent "open with", you have to configure ShellNoUseStoreOpenWith_1 for that additionally.
RemoveWindowsUpdate_ICM: While this setting does not prevent Store applications from updating, it does prevent the user from adding optional features (including language packs) and from searching for updates online.
When 'System' is selected as the installation context for UWP applications using the Microsoft Store (new) method in Intune, they are added to the operating system's provisioned packages. This means that applications installed this way will survive a wipe (with no options selected), a fresh start, and an Autopilot reset. However, after these actions, the application will appear as if uninstalled in the company portal, even though it is installed and available to the user.

Store updates are a cloud service. As such, if working with a proxy or firewall, the following URLs need to be reachable in both the system and user context.