IP Restrictions are possible for Azure Websites as is protecting the site with Basic Authentication..
Are these, or any other web.config techniques possible on Azure Fu
Web.config files do not apply to Function Apps and will indeed (as you found) be ignored.
Because of this limitation, features that require web.config customization are not supported with the standard Function App model (as you can see in the answer linked by @Mikhail, there are workarounds), and the alternative, currently, would be to handle this requirement in code.