Allow 'paths' without 'baseUrl' (#40101)

* Allow paths without baseUrl

* Remove exception for leading * paths

* Add comment, remove commented code

* Update baselines

* Remove unnecessary default

* Fix test harness

* Fix baseline

* Resolve relative to host.getCurrentDirectory() with createProgram API

src/compiler/commandLineParser.ts

@@ -2509,6 +2509,13 @@ namespace ts {
             parseOwnConfigOfJson(json, host, basePath, configFileName, errors) :
             parseOwnConfigOfJsonSourceFile(sourceFile!, host, basePath, configFileName, errors);
 
+        if (ownConfig.options?.paths) {
+            // If we end up needing to resolve relative paths from 'paths' relative to
+            // the config file location, we'll need to know where that config file was.
+            // Since 'paths' can be inherited from an extended config in another directory,
+            // we wouldn't know which directory to use unless we store it here.
+            ownConfig.options.pathsBasePath = basePath;
+        }
         if (ownConfig.extendedConfigPath) {
             // copy the resolution stack so it is never reused between branches in potential diamond-problem scenarios.
             resolutionStack = resolutionStack.concat([resolvedPath]);