Desktop GUI agents operate under partial observability: visually similar screens can correspond to different underlying workflow states, so locally plausible actions can lead to sharply different outcomes. We frame this as a problem of computer/OS state exploration, where effective behavior requires both expanding the reachable frontier and reducing ambiguity before committing. We present ScreenSearch, a system that combines structural screen retrieval and deduplication with an ambiguity-aware PUCT graph-bandit for large-scale desktop exploration. The retrieval layer converts UIA trees into location-aware structural features, indexes related screens through sparse token search and metadata filters, and maintains a shared deduplicated state graph across VM workers. On top of this graph, we define a scalable ambiguity signal based on matched-action outcome dispersion. If similar screens produce different next states under the same action signature, the state should be probed further rather than treated as resolved. We use this signal together with frontier rewards to drive large-scale exploration and replay-start policy evaluation over the shared graph. Across 11 desktop applications, ScreenSearch collects over 1M screenshots and over 30K deduplicated states, yielding large exploration corpora with substantial cross-application and within-application diversity. On a fixed replay-start slice, we observe a clear novelty--ambiguity trade-off: some policies reduce ambiguity quickly while discovering little frontier. Ambiguity reduction alone is therefore not a sufficient exploration objective. Appendix ablations show that stronger proposal priors can materially improve unique-state discovery during corpus building. These results suggest that state identity, proposal quality, and ambiguity-aware search all matter when deciding when to probe and when to commit.