So, the best option is to reinstall your client. If you are able to access your account from the browser, then the problem lies within the Steam client.
Restart your Client or PC: You may try to close all the steam-related APIs running in the background through the task. Steam Web & Reinstall Steam Client: As it is a login-based connection issue, make sure whether you can get inside your account from your web browser. Solutions to fix Steam Verifying Login Information Error Swapping Online/Offline: The other notable working solution is to toggle from Online to Offline.Restart your Client or PC: You may try to close all the steam-related APIs running in the background through the task manager and restart the Steam client.The only downside to the solution is that the bug may appear after some time. When the client restarts under the offline mode, switch it back to Online again.
To do this, launch the client and click on the 'Go Offline' option.