feat(owlry-core): move backend modules from owlry

Move the following modules from crates/owlry/src/ to crates/owlry-core/src/:
- config/ (configuration loading and types)
- data/ (frecency store)
- filter.rs (provider filtering and prefix parsing)
- notify.rs (desktop notifications)
- paths.rs (XDG path handling)
- plugins/ (plugin system: native loader, manifest, registry, runtime loader, Lua API)
- providers/ (provider trait, manager, application, command, native_provider, lua_provider)

Notable changes from the original:
- providers/mod.rs: ProviderManager constructor changed from with_native_plugins()
  to new(core_providers, native_providers) to decouple from DmenuProvider
  (which stays in owlry as a UI concern)
- plugins/mod.rs: commands module removed (stays in owlry as CLI concern)
- Added thiserror and tempfile dependencies to owlry-core Cargo.toml

crates/owlry-core/src/plugins/api/mod.rs

@@ -0,0 +1,77 @@
+//! Lua API implementations for plugins
+//!
+//! This module provides the `owlry` global table and its submodules
+//! that plugins can use to interact with owlry.
+
+pub mod action;
+mod cache;
+pub mod hook;
+mod http;
+mod math;
+mod process;
+pub mod provider;
+pub mod theme;
+mod utils;
+
+use mlua::{Lua, Result as LuaResult};
+
+pub use action::ActionRegistration;
+pub use hook::HookEvent;
+pub use provider::ProviderRegistration;
+pub use theme::ThemeRegistration;
+
+/// Register all owlry APIs in the Lua runtime
+///
+/// This creates the `owlry` global table with all available APIs:
+/// - `owlry.log.*` - Logging functions
+/// - `owlry.path.*` - XDG path helpers
+/// - `owlry.fs.*` - Filesystem operations
+/// - `owlry.json.*` - JSON encode/decode
+/// - `owlry.provider.*` - Provider registration
+/// - `owlry.process.*` - Process execution
+/// - `owlry.env.*` - Environment variables
+/// - `owlry.http.*` - HTTP client
+/// - `owlry.cache.*` - In-memory caching
+/// - `owlry.math.*` - Math expression evaluation
+/// - `owlry.hook.*` - Event hooks
+/// - `owlry.action.*` - Custom actions
+/// - `owlry.theme.*` - Theme registration
+pub fn register_apis(lua: &Lua, plugin_dir: &std::path::Path, plugin_id: &str) -> LuaResult<()> {
+    let globals = lua.globals();
+
+    // Create the main owlry table
+    let owlry = lua.create_table()?;
+
+    // Register utility APIs (log, path, fs, json)
+    utils::register_log_api(lua, &owlry)?;
+    utils::register_path_api(lua, &owlry, plugin_dir)?;
+    utils::register_fs_api(lua, &owlry, plugin_dir)?;
+    utils::register_json_api(lua, &owlry)?;
+
+    // Register provider API
+    provider::register_provider_api(lua, &owlry)?;
+
+    // Register extended APIs (Phase 3)
+    process::register_process_api(lua, &owlry)?;
+    process::register_env_api(lua, &owlry)?;
+    http::register_http_api(lua, &owlry)?;
+    cache::register_cache_api(lua, &owlry)?;
+    math::register_math_api(lua, &owlry)?;
+
+    // Register Phase 4 APIs (hooks, actions, themes)
+    hook::register_hook_api(lua, &owlry, plugin_id)?;
+    action::register_action_api(lua, &owlry, plugin_id)?;
+    theme::register_theme_api(lua, &owlry, plugin_id, plugin_dir)?;
+
+    // Set owlry as global
+    globals.set("owlry", owlry)?;
+
+    Ok(())
+}
+
+/// Get provider registrations from the Lua runtime
+///
+/// Returns all providers that were registered via `owlry.provider.register()`
+pub fn get_provider_registrations(lua: &Lua) -> LuaResult<Vec<ProviderRegistration>> {
+    provider::get_registrations(lua)
+}