Hi,
i noticed, that only passwords are depreciated soon.
Basic authentication using a password to Git is deprecated and will soon no longer work. Visit https://github.blog/2020-12-15-token-authentication-requirements-for-git-operations/ for more information around suggested workarounds and removal dates.
Is web browser login affected too?
How can I use token authentication without android, ios, simcard/phone?
Only with linux (ubuntu) devices and mail.
This message is not about browser login, it’s about Git over HTTPS and API access. Simply put, for Git operations you’ll need to use a Personal Access Token (PAT) instead of your password.
Documentation on how to create the PAT is here, for pulling/fetching and pushing the repo and (if you use Actions) workflow scopes should be enough:
It’s generally a good idea to store the PAT in a password manager, because it’s not easy to remember. 
Hi @ka223, welcome to the community.
Correct rather than the password option to authenticate Git operations today, you must begin using a personal access token or SSH key, but neither theses options involve GitHub Two Factor Authentication (2FA), so do not involve a 2FA device such as Android, IOS, simcard/phone.
All these alternative options are available already.
You can follow the GitHub docs which provide a step-by-step guide for creating a personal access token and/or an SSH key for Git access.
There is also a Sign In With Browser (web auth flow) for Git you can use, if you prefer.
Your normal browser GUI login behaviour will continue to work as it does today