Are there any routers that can simultaneously work in two modes - 1. access point and 2. the client wireless network. Ie the router itself is connected to Wi-Fi network and to the Internet and then distributes the Internet to its customers.
Is it possible to turn on MicroTik or Raspberry Pie?
For example TP-Link can do that, you need a suitable router with 2 wi-fi modules. On Mikrotik or any computer that can be done if you put 2 wifi cards.