I am facing a critical error while publishing posts

Redirection and having to login again are two separate issues. There is likely an issue with your browser sending auth cookies if you continually have to login. The only reason I can think of for it not being a browser issue is if some theme or plugin process is automatically logging you out. A security plugin perhaps?

The redirection is likely due to your theme or a plugin. As a test, deactivate all plugins and switch to a default Twenty* theme. You should no longer be redirected and maybe you’ll even stay logged in. Identify the module responsible by restoring your normal theme and plugins, one at a time, testing after each. When the undesired behavior returns, the last activated module was the cause.