feat: Text input system for DCSS webtiles protocol

[willthehuman]

Summary

• Fixed protocol message: sendTextInput now sends {"msg": "input", "text": "..."} instead of the incorrect {"msg": "text_input", "text": "..."}, matching the DCSS webtiles specification for text input submission
• Added keyboard type switching: Shows numeric keyboard with digits-only filter for number input type; standard keyboard for text and seed/seed-selection types
• Repositioned overlay: Changed from a centered full-screen overlay to a bottom-aligned floating panel that sits above the software keyboard using MediaQuery.viewInsets.bottom, allowing partial game view visibility through a reduced-opacity backdrop

Context

The DCSS server sends init_input/close_input/update_input messages for free-text entry (character naming, chat, menu search, drop counts). The protocol parsing, game state management (TextInputState), and game screen wiring were already implemented. This PR fixes the outgoing message format and improves the overlay UX for mobile.

Test plan

• Connect to a DCSS server and start a new game — verify the character naming prompt appears as a bottom-aligned panel
• Enter a character name and submit — verify the name is accepted by the server
• Press Cancel on the overlay — verify it sends ESC (keycode 27) and dismisses
• Trigger a "drop how many?" prompt — verify numeric keyboard appears
• Verify update_input from server updates the text field content
• Verify the overlay positions correctly above the software keyboard on both iOS and Android

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