Problems: auto-fix & problem panel (#541)

Test cases:
- [x] create-ts-errors
  - [x] with auto-fix
  - [x] without auto-fix 
- [x] create-unfixable-ts-errors
- [x] manually edit file & click recheck
- [x] fix all
- [x] delete and rename case

THINGS
- [x] error handling for checkProblems isn't working as expected
- [x] make sure it works for both default templates (add tests) 
- [x] fix bad animation
- [x] change file context (prompt/files)

IF everything passes in Windows AND defensive try catch... then enable
by default
- [x] enable auto-fix by default

src/shared/problem_prompt.ts

@@ -0,0 +1,24 @@
+import type { ProblemReport } from "../ipc/ipc_types";
+
+/**
+ * Creates a more concise version of the problem fix prompt for cases where
+ * brevity is preferred.
+ */
+export function createProblemFixPrompt(problemReport: ProblemReport): string {
+  const { problems } = problemReport;
+
+  if (problems.length === 0) {
+    return "No TypeScript problems detected.";
+  }
+
+  const totalProblems = problems.length;
+  let prompt = `Fix these ${totalProblems} TypeScript compile-time error${totalProblems === 1 ? "" : "s"}:\n\n`;
+
+  problems.forEach((problem, index) => {
+    prompt += `${index + 1}. ${problem.file}:${problem.line}:${problem.column} - ${problem.message} (TS${problem.code})\n`;
+  });
+
+  prompt += "\nPlease fix all errors in a concise way.";
+
+  return prompt;
+}