Word custom dictionary is a text file you can save and replace on new systems. interwebs say[1] it's here: C:\Users\username\AppData\Roaming\Microsoft\UProof\CUSTOM.DIC
Just grab a copy of that and store it in your "Documents" folder (or cloud) since your "support" folk might be forgetting to save that directory. Then you can copy it back on the new computer.
Similarly, interwebs says[1] your autocomplete is stored in two places. A .acl file here: C:\Users\username\AppData\Roaming\Microsoft\Office
and the normal.dotm file here:
C:\Users\username\AppData\Roaming\Microsoft\Templates

warning: the autocorrect might not transfer clean due to version differences, so backup any files replaced in case you need to revert back.

1: not in a position at the moment to verify this, but it sounds right
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