Replace free-text encounter method input with dropdown selector

Use the predefined METHOD_ORDER/METHOD_CONFIG from EncounterMethodBadge
to populate a select dropdown with all known encounter methods plus an
"Other" option for custom values. Shows a colored badge preview on
selection. Correctly handles editing encounters with non-standard methods.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

.beans/nuzlocke-tracker-8w9s--gauntlet-rule-option-for-genlockes.md

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+---
+# nuzlocke-tracker-8w9s
+title: Gauntlet rule option for genlockes
+status: draft
+type: feature
+created_at: 2026-02-08T19:15:43Z
+updated_at: 2026-02-08T19:15:43Z
+parent: nuzlocke-tracker-25mh
+---
+
+Add an optional **Gauntlet** rule for genlocke runs. When enabled, Pokemon that enter the Hall of Fame at the end of a leg are NOT transferred to the next game — instead, they (and their evolutionary families) are added to the dupe list for subsequent legs.
+
+## Behavior
+- Toggled as an optional rule when creating/editing a genlocke
+- When a leg is completed, surviving Hall of Fame Pokemon are marked as "dupes" for the next leg rather than being transferred as eggs/starters
+- This means the player cannot catch anything in those evolutionary lines in future legs (standard dupe clause enforcement)
+- The cumulative dupe list grows with each completed leg
+- Effectively forces the player to use entirely new Pokemon each generation
+
+## Notes
+- This is a variant of the standard genlocke format that increases difficulty
+- The dupe list should track evolutionary families, not just the specific Pokemon (e.g., if Charizard is in the HoF, Charmander and Charmeleon are also duped)
+- Should integrate with the existing dupe clause system already in the tracker
+- Consider showing the cumulative gauntlet dupe list somewhere in the genlocke dashboard