Can I search the repository for an entry with a stamp?
Yes, you can using Advanced Search Syntax.
Here's a document with lots of details of how to complete advanced search syntax queries: https://support.laserfiche.com/resources/3920/advanced-search-syntax-10-3
A couple examples from that document:
Search for stamps (page 41): {LF:AnnType="S"}
Search for stamps named "TEST" (page 45): {LF:AnnStampName= “TEST”}
EDIT TO ADD: These do work beyon version 10.3 - they just haven't made major changes since that version, so the document hasn't needed to be updated since then (or so I've been told on other LFAnswer posts).
Confirming the above. The Advanced Search Syntax 10.3 documentation guide is still valid for subsequent versions (through the current latest release of Laserfiche Server 11 at least). I believe we have updating the title and date on that guide buried somewhere in the To-Do list.