Fix dead links in docs (#10097)

Co-authored-by: Guangcong Luo <[email protected]>

ARCHITECTURE.md

@@ -3,12 +3,11 @@ Pokemon Showdown architecture
 
 At the highest level, PS is split into three parts:
 
-- Client
-- Login server
-- Game server
-
-The game server is in this repository, **[smogon/pokemon-showdown](https://github.com/smogon/pokemon-showdown)**, while the client and login server are in **[smogon/pokemon-showdown-client](https://github.com/smogon/pokemon-showdown-client)**. All three communicate directly with each other.
+- Game server (**[smogon/pokemon-showdown](https://github.com/smogon/pokemon-showdown)**)
+- Client (**[smogon/pokemon-showdown-client](https://github.com/smogon/pokemon-showdown-client)**)
+- Login server (**[smogon/pokemon-showdown-loginserver](https://github.com/smogon/pokemon-showdown-loginserver)**)
 
+All three communicate directly with each other.
 
 Game server
 -----------
@@ -25,22 +24,20 @@ Its entry point is [server/index.ts](./server/index.ts), which launches several
 
 - [server/chat.ts](./server/chat.ts) sets up `Chat`, which handles chat commands and messages coming in from users (all client-to-server commands are routed through there)
 
-`Rooms` also includes support for battle rooms, which is where the game simulation itself is done. Game simulation code is in [sim/](./sim/).
-
+`Rooms` also includes support for battle rooms, which is where the server connects to the game simulator itself. Game simulation code is in [sim/](./sim/).
 
 Client
 ------
 
 The client is built in a mix of TypeScript and JavaScript, with a mostly hand-rolled framework built on Backbone. There’s a rewrite to migrate it to Preact but it’s very stalled.
 
-Its entry point is [index.template.html](https://github.com/smogon/pokemon-showdown-client/blob/master/index.template.html).
-
-It was written long ago, so instead of a single JS entry point, it includes a lot of JS files. Everything important is launched from [js/client.js](https://github.com/smogon/pokemon-showdown-client/blob/master/js/client.js).
+Its entry point is [index.template.html](https://github.com/smogon/pokemon-showdown-client/blob/master/play.pokemonshowdown.com/index.template.html)
 
+It was written long ago, so instead of a single JS entry point, it includes a lot of JS files. Everything important is launched from [js/client.js](https://github.com/smogon/pokemon-showdown-client/blob/master/play.pokemonshowdown.com/js/client.js)
 
 Login server
 ------------
 
-The client’s login server, which handles logins and most database interaction, is written in PHP, with a rewrite to TypeScript in progress. The backend is split between a MySQL InnoDB database and a Percona database, with a migration to Postgres planned.
+The client’s login server, which handles logins and most database interaction, is written in TypeScript in progress. The backend is split between a MySQL InnoDB database (for most things) and a Postgres database (for Replays).
 
-Its entry point is [action.php](https://github.com/smogon/pokemon-showdown-client/blob/master/action.php).
+Its entry point is [server.ts](https://github.com/smogon/pokemon-showdown-loginserver/blob/master/src/server.ts).