Is there a checklist/best practices that I can use to make sure password change will not impact the platform negatively?

You have a question if there is a checklist/best practices that you can use to make sure password change will not impact the platform negatively? You are not aware of anything on your platform that could be using these credentials.

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There is no root cause for this as this is just a question or thought process evaluating what are all those areas that will be impacted when an admin user's password is changed and if there is any best practice checklist to quickly recognize this.

Considering this scenario, you can quickly identify this following below steps:

1. Go to System Logs > Transactions
2. Filter the list with Created by with the User Id of example user (admin in this case)
3. This will filter the list with all the transactions made by that user.
4. Checking the Type and URL columns values you can recognize if this transactions are interactive (Type is Form/List) or used by any integrations (SOAP/REST/JSON etc.)

This approach will assist you answering your question and other than this there is no such best practice checklist defined for this.