iMessage not syncing after password change

Click on ok from iPhone see the articles Use Messages in iCloud - Apple Support

Set up iCloud for Messages on all your devices - Apple Support

Change iMessage preferences in Messages on Mac - Apple Support

Click on sync now .

Open messages preferences in Mac the settings must be as per screen shot .

Is there any more devices like iPhone / iPad / another Mac signed in with same Apple ID and password on the same network .

Make sure if there are two Macs synced , their admin password should not be same .

If its a single Mac see an article If you can't sign in to your iMessage account or FaceTime on your Mac - Apple Support

A query what is method of signing Apple ID in iPhone and Mac .

If you have created a web mail address say with gmail services https://support.google.com/mail/answer/56256?hl=en and its mail address and password should be exactly same as Apple ID and password signed in Mac system preferences , say its example1@gmail.com , and this id should also be signed in your iPhone on the same network the enable this account , will appear in mail preferences , you must not use only iCloud web based account Web-only access to iCloud - Apple Support

In fact you had created multiple accounts from Mac system preferences > internet accounts its ok they can be added , but the way of signing Apple ID is different in your Mac .

See the articles How to create a new Apple ID - Apple Support

Sign in with your Apple ID - Apple Support

Note : whenever an Apple ID or its password is changed from Mac , if other iPhone is synced the Apple ID ( here only Apple ID is going to be changed ) it has to be updated from iPhone What to do after you change your Apple ID or password - Apple Support

Are you using 2FA or secondary authentication account ?

If secondary authentication account is set there will be option button in front of keychain box , try to set up iCloud Keychain .

See the article If iCloud Keychain won't turn on or sync - Apple Support

If iCloud Keychain is corrupted in Mac .

( a ) Use an iPhone and sign in with same Apple ID and password in your Mac .

( b ) In iPhone go to settings , iCloud open keychain and click on advanced two options will be shown reset code and reset iCloud Keychain , click on reset iCloud Keychain .

( c ) A verification code will appear on your mobile number through sms and it will prompt to generate a code , think of code and fill up in the field so keychain will be set up in iPhone , write down this code .

( d ) Come to Mac in system preferences > click on iCloud the box of keychain is unchecked , so tap the keychain box , it will show waiting for approval click on option button , enter the passcode that is generated in iPhone , click on confirm .

( e ) Again in iPhone a pop up will appear showing approve or deny for name of Mac to approve for keychain , click on allow .

( f ) In Mac click on option button enter trusted number an sms will come having a verification code , enter it the trusted number will be saved and visible and finally keychain is set in Mac .

Your email address and its password should be exactly same as Apple ID mail address and its password .

What is apple login password ? is it an admin password to sign in Mac , that should be totally different .

Read some articles Tips for creating secure passwords on Mac - Apple Support

Learn how passwords are used on Mac - Apple Support

Uncheck the box of handoff from Mac system preferences > general , and also from iPhone Pick up where you left off with Handoff on Mac - Apple Support

Changing admin password has no connection with it , the term and conditions should be enabled .

In Mac system prefernces at present an Apple ID say example1@icloud.com is signed , keychain box is checked and there is no option button in front of it as 2FA is permanently enabled , in case if secondary authentication would have set option button appears in front of keychain box .

In internet account see both gmail account and iCloud account are set up , its the choice of user to change apple id .

If both gmail account / iCloud account are configured the messages will sync and in message preferences enable account will always appear , so my question from you is it the same way you have set up the accounts ?

Your mail address say example2@hotmail.com and its password should be exactly same as Apple ID and password signed in Mac system preferences .

In this way both hotmail account and iCloud account will be configured .

This is the only way to sync from Mac , you can't neglect iCloud account services , in your iPhone exactly the same Apple ID and password should be signed in on the same network , don't use any VPN services a simple broad band network connection issued from your internet service provider is sufficient .

contact apple support Contact Apple for support and service - Apple Support

Can you please post a screen shot appearing , make sure you hide the mail address and phone number when posting here .