Local sites must use VirtualHost, as with all hosting providers.
See:
The need for Virtual Hostand
Wampserver 3 - Create or add a VirtualHostWhat's more, WordPress writes its own URL to its database, so you need to modify the database to include the local url.
Switching local sites to https can't be done simply by copying files - you need to modify the local server to do this - but only after the local sites are running correctly as VirtualHost in http mode.
See: Right-Click -> Help -> Wampserver HTTPS mode help
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Documentation Apache -
Documentation PHP -
Documentation MySQL -
Wampserver install files & addons