I haven't used Outlook for about 3 years. When my MS Office (now called
MS 365) 5-year subscription ran out, I decided not to renew. I don't
have Outlook, especially not back to 2003, to check how the
Auto-Complete list is implemented, so I had to search online.
The addresses you mention is called the Auto-Complete list. See:
https://learn.microsoft.com/en-us/outlook/troubleshoot/contacts/information-about-the-outlook-autocomplete-list
https://www.slipstick.com/outlook/email/understanding-outlooks-autocomplete-cache-nk2/
As mentioned in that article, is the "Suggest names while completing To,
Cc, and Bcc fields" enabled? That won't restore the auto-complete cache
before, but, if you find it useful, you should enable it now.
Is there an .nk2 file in your old Outlook profile folder that you copied
to the new computer? Does it have permissions from your new Windows
account, not for your old Windows account?
https://www.nirsoft.net/utils/outlook_nk2_edit.html
That lets you export the nickname file to another format, and maybe that
format can be imported in the new .nk2 file; however, I don't remember
there is an import function for the AutoComplete cache.
For a copy of the old .nk2 file that you saved on the new computer (in a
temp folder), you could use a hex editor to see if there are records
stored in there, or if it is blank. The hex editor should show both the
hex values of every byte along with the text characters. Check if you
can see some text that stores e-mail addresses. No point in migrating
an empty .nk2 file to the new computer.
https://portalvhds6gyn3khqwmgzd.blob.core.windows.net/files/NK2/NK2WithBinaryExample.pdf
That describe the binary structure of the .nk2 file.
I'm not sure just copying over the profile file will work. You got it
from one Windows account to copy on a different host under a different
Windows account. Even if you use the same username for the accounts on
the old and new computer, they are not equivalent or compatible
accounts. The SID (Security Identifier) and permissions will differ.
Probably the proper way to import the old profile is to copy the old
profile folder to a temp place on the new computer, and then use the
import functions of Outlook on the new computer.
https://itstillworks.com/completely-reset-google-chrome-15672.html
https://www.wintips.org/how-to-create-a-new-outlook-profile-and-import-outlook-pst/