Based on your post, I understand that some people profile photos are not showing in the organization chart web part.
I did a test in my end, the newly added user's profile photo can display well in the organization chart web part.
First, please try the resolutions provide by the official article to check the behavior.
For your reference: https://learn.microsoft.com/en-us/sharepoint/troubleshoot/administration/profile-picture-not-showing
Besides, sometimes network or browser cache can cause pictures not to be displayed, please try following suggestions to see if they can work:
1.Switch to another network, disable proxy.
2.Clear the browser cache.
3.Try to use another browser.
4.Start your browser in private/incognito mode.
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