You had deleted both your mail account ( like gmail ) and iCloud account from the location system preferences - internet accounts when you try to add them ( click on plus sign ) they will not be added as they are configured with web server but not with Mac .
to set up these accounts see this method Method to sign out from iCloud account .
Even if you create a new test user account , the iCloud Keychain verification code will be required see this article How to test an issue in another user account on your Mac - Apple Support
See the manual method -
HOW TO SET UP A NEW TEST USER ACCOUNT
Create a new user account in users and groups by clicking on plus sign , name an account and enter its password .
Take cursor on apple logo and log out from your old user account and then enter the credentials name and password on the screen of your new user account .
( a )The window is showing data and privacy , click on continue and sign in with your Apple ID ( fill up the credentials ) and click on continue .
( b ) Again enter your Apple ID and password and click on continue .
( c ) A prompt will appear on the screen use two factor authentication ( its optional you can uncheck the box and click on continue ) .
( d ) A pop up window will appear do not upgrade Apple ID security and upgrade iCloud security , so click on do not upgrade .
( e ) A small circle will be rotating , setting up account will be shown , wait for a while and options will be shown would you like to set up iCloud Keychain ( 1 ) set up iCloud Keychain ( 2 ) set up later , you can click on set up later and click on continue .
( f ) A window will appear showing enable ask Siri , keep the box checked and click on continue .
( g ) Another window will appear all your files in iCloud stores files from documents and desktop in iCloud Drive , so check the box of it and click on continue .It will show setting up your Mac , three right check marks will be shown .
( h ) Open system preferences and click on accessibility > trackpad options , check the boxes of scrolling with inertia and enable dragging with three finger drag and click on ok ( as drag and drop feature always help a user in every way ) .
( I ) Again in the system preferences > click on I cloud you will see the box of keychain is unchecked , so check the box of it after a while a prompt will appear enter you Apple ID password to set up iCloud Keychain so fill up the password and click on ok .
( j ) Again a pop up window will appear to set up iCloud keychain on this Mac , request approval from one of your other devices using iCloud Keychain .( 1 ) use code ( 2 ) cancel ( 3 ) request approval , so click on use code .
( k ) Wait for a while , nothing will appear on the screen after that a window will appear enter your iCloud security code , so after entering it click on next .
( l) An sms will come to the trusted mobile so enter the code and click on ok and you will notice in front of keychain setting up and a small circle is rotating , the box of keychain will get checked .
( m) On the top right corner of the screen a small notification will appear google password required ( in your case it depends which sevices are being used yahoo , hotmail or other ) .
( n ) Enter your gmail password and click on next , finally iCloud Keychain is set up in the new user account you can open mail application and click on get mail icon all mails will start downloading from the server .
( o ) Open notes application and click on continue all notes data saved in iCloud and in all google will start downloading and it will take time to download ( high network speed is essential ) .
( p ) Then open calendar and click on continue , click on view and show calendar list .
If you want to transfer pictures , movies , music , downloads contents from the home folder of first user account to the second user account .
Open pictures and press command and info change the permissions to read only the folder pictures will be unlocked , them drag and drop the folder on the desktop automatically you can view the contents of pictures in the second user account .
Note : if your web mail account is configured with apple mail application , notes , calendars , contacts , photos are saved in iCloud and web server in the new user account they will definitely sync , you can create a new user account and don't delete the old user account and post back what're the results .
