Hi Kimaldave,
We see that when trying to use macOS Recovery to reinstall the macOS you are prompted to connect to the internet to finish the install. Being able to complete the install and have access to your Mac again is important. You've come to the right place for help.
Are you connected to your personal Wi-Fi network? Did you choose to "Reinstall macOS Big Sur from the startup screen? Check out the link below for steps to set finish recovery on your Mac.
How to reinstall macOS
Additional information about your Mac model and the network connection will help further if it continues.
Have a good day!