refactor(bot): split storage.rs into storage/{memory,redis,sqlite,mod}

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Summary

bot/storage.rs had grown to 417 lines holding three unrelated
concerns behind a single file:

• the always-on StateStore trait with its default method
  implementations (get/set/remove plus exists/ttl/keys/
  remove_prefix/get_many/set_many);
• the always-on MemoryStateStore (HashMap + Entry with
  Instant-based TTL);
• two feature-gated backends: RedisStateStore behind bot-redis
  (redis::Commands, SCAN/SETEX/Pipeline) and SqliteStateStore
  behind bot-sqlite (rusqlite with an expires_at column).

Split along those natural boundaries per the AGENTS.md guideline
("split files when a module grows beyond ~400-600 lines or mixes
multiple responsibilities"):

• storage/mod.rs - the StateStore trait with its default impls,
  the module wiring, and the public re-exports (MemoryStateStore
  always, RedisStateStore gated by bot-redis, SqliteStateStore
  gated by bot-sqlite).
• storage/memory.rs - Entry + MemoryStateStore + its trait impl.
• storage/redis_store.rs - RedisStateStore + its trait impl,
  gated behind bot-redis. Named *_store to avoid colliding with
  the redis crate name inside the module namespace.
• storage/sqlite_store.rs - SqliteStateStore + its trait impl,
  gated behind bot-sqlite. Same *_store suffix for symmetry.

External call sites are unchanged

bot/mod.rs kept its re-exports exactly as they were:

pub use storage::{MemoryStateStore, StateStore};
#[cfg(feature = "bot-redis")]
pub use storage::RedisStateStore;
#[cfg(feature = "bot-sqlite")]
pub use storage::SqliteStateStore;

So bot::{MemoryStateStore, StateStore, RedisStateStore, SqliteStateStore} continue to resolve and the public surface is
bit-for-bit identical. The 9 call sites across the bot (runtime.rs,
runtime_async.rs, scheduler.rs, scheduler_async.rs, fsm.rs,
context.rs, app.rs, router/dispatch.rs, lib.rs) compile
unchanged.

Structural only, no semantic change

• Trait method bodies for all three impls are byte-for-byte identical
  to the pre-split file.
• TTL handling identical: Instant+Entry for memory, SETEX for
  Redis, datetime('now') + expires_at column for SQLite.
• Feature gates identical - trait + memory always on, Redis behind
  bot-redis, SQLite behind bot-sqlite.
• MemoryStateStore::new and the StateStore trait gained brief doc
  comments on individual methods (required by missing_docs = "deny"
  now that they are in their own file); no behavioral effect.

Local verification:

• cargo fmt --all --check clean
• cargo clippy --workspace --all-targets --all-features -- -D warnings clean
• cargo test --workspace --all-features -> 287 passed / 0 failed

Review & Testing Checklist for Human

• Spot-check storage/mod.rs re-exports: bot::MemoryStateStore,
  bot::StateStore, and the feature-gated bot::RedisStateStore
  / bot::SqliteStateStore must all still resolve from downstream
  crates. grep -rn "::MemoryStateStore\|::StateStore\|::RedisStateStore\|::SqliteStateStore" crates/teamtalk
  reproduces the full call surface.
• Confirm the *_store suffix on the Redis and SQLite module
  files is acceptable (the alternative is mod redis; /
  mod sqlite; which shadows the external crate names inside
  the bot namespace - a wart I'd rather avoid).
• Confirm #[cfg(feature = "bot-redis")] and
  #[cfg(feature = "bot-sqlite")] still correctly gate the
  backend modules (both at the mod declaration in
  storage/mod.rs and at the pub use line).

Notes

This is the next PR in the P0 structural refactor queue after #44
(dedupe can_issue_logged_in_command), #45 (extract
poll_command_completion), and #46 (split client/bus.rs). Next up:
bot/fsm.rs (559 lines), then client/hooks/builders.rs (574 lines),
types/entities/media_common.rs (458 lines), and the
client/backend.rs (1334 lines) + client/backend_mock.rs (1101
lines) pair.

Branches from clean main; I'm queueing all of these as independent
PRs against main so you can merge them in whatever order suits. If
any touch the same file I'll rebase the later one once its predecessor
lands.

The pre-existing semver CI gate is expected to remain red;
release-plz handles the eventual version bump. Every other check is
expected to pass.

Link to Devin session: https://app.devin.ai/sessions/71fdd6196cb74723a2e277bb81993a9c
Requested by: @BlindMaster24

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✅ Devin Review: No Issues Found

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