[AI Assistance] Refactor AiAgent

Removes some unnecessary methods and orders the methods by public/protected/private ordering changing the specifier when
needed.

Bug: 393267670
Change-Id: I246a10cda24ea8bd1678e6db801d12d62ee5aa0e
Reviewed-on: https://chromium-review.googlesource.com/c/devtools/devtools-frontend/+/6235284
Reviewed-by: Nikolay Vitkov <[email protected]>
Commit-Queue: Alex Rudenko <[email protected]>

Author: OrKoN

front_end/panels/ai_assistance/agents/AiAgent.test.ts

@@ -303,7 +303,7 @@ describeWithEnvironment('AiAgent', () => {
 
         await Array.fromAsync(agent.run('query', {selected: mockConversationContext()}));
 
-        assert.deepEqual(agent.chatHistoryForTesting, [
+        assert.deepEqual(agent.buildRequest({text: ''}, Host.AidaClient.Role.USER).historical_contexts, [
           {
             role: Host.AidaClient.Role.USER,
             parts: [{text: 'query'}],