fix(server): suffix-fallback auto-named branches and rotate opencode waterfall

Auto-namer now probes refs/heads/<name> and appends -2, -3, … (up to 50)
when the desired slug is taken, instead of failing with "branch already
exists" and leaving the worktree on its placeholder name.

Structured-generation waterfall replaces opencode/gpt-5-nano with
opencode/minimax-m2.5-free and opencode/nemotron-3-super-free so users
without nano configured fall through to free models they actually have.

packages/server/src/server/agent/agent-response-loop.ts

@@ -96,7 +96,8 @@ export interface StructuredAgentGenerationWithFallbackOptions<T> {
 export const DEFAULT_STRUCTURED_GENERATION_PROVIDERS: readonly StructuredGenerationProvider[] = [
   { provider: "claude", model: "haiku" },
   { provider: "codex", model: "gpt-5.4-mini", thinkingOptionId: "low" },
-  { provider: "opencode", model: "opencode/gpt-5-nano" },
+  { provider: "opencode", model: "opencode/minimax-m2.5-free" },
+  { provider: "opencode", model: "opencode/nemotron-3-super-free" },
 ] as const;
 
 interface SchemaValidator<T> {

packages/server/src/server/paseo-worktree-service.test.ts

@@ -173,6 +173,44 @@ test("renames an eligible unnamed branch-off worktree once on first agent contex
   expect(branchAfterSecond).toBe("renamed-from-agent-context");
 });
 
+test("falls back to a numeric suffix when the desired branch name already exists", async () => {
+  const { repoDir, tempDir } = createGitRepo();
+  cleanupPaths.push(tempDir);
+
+  execFileSync("git", ["branch", "renamed-from-agent-context"], { cwd: repoDir, stdio: "pipe" });
+  execFileSync("git", ["branch", "renamed-from-agent-context-2"], { cwd: repoDir, stdio: "pipe" });
+
+  const created = await createPaseoWorktree(
+    {
+      cwd: repoDir,
+      worktreeSlug: "dazzling-yak",
+      runSetup: false,
+      paseoHome: path.join(tempDir, ".paseo"),
+    },
+    createDeps(),
+  );
+
+  const result = await attemptFirstAgentBranchAutoName({
+    cwd: created.worktree.worktreePath,
+    firstAgentContext: { prompt: "Build the agent context name" },
+    generateBranchNameFromContext: async () => "renamed-from-agent-context",
+  });
+
+  expect(result).toEqual({
+    attempted: true,
+    renamed: true,
+    branchName: "renamed-from-agent-context-3",
+  });
+  expect(
+    execFileSync("git", ["branch", "--show-current"], {
+      cwd: created.worktree.worktreePath,
+      stdio: "pipe",
+    })
+      .toString()
+      .trim(),
+  ).toBe("renamed-from-agent-context-3");
+});
+
 test("renames the branch even when the app supplies a random placeholder slug", async () => {
   const { repoDir, tempDir } = createGitRepo();
   cleanupPaths.push(tempDir);

packages/server/src/server/paseo-worktree-service.ts

@@ -13,7 +13,7 @@ import {
   type CreateWorktreeCoreInput,
 } from "./worktree-core.js";
 import { validateBranchSlug, type WorktreeConfig } from "../utils/worktree.js";
-import { getCurrentBranch, renameCurrentBranch } from "../utils/checkout-git.js";
+import { getCurrentBranch, localBranchExists, renameCurrentBranch } from "../utils/checkout-git.js";
 import {
   markPaseoWorktreeFirstAgentBranchAutoNameAttempted,
   readPaseoWorktreeMetadata,
@@ -85,6 +85,7 @@ export async function attemptFirstAgentBranchAutoName(options: {
   }) => Promise<string | null>;
   getCurrentBranch?: typeof getCurrentBranch;
   renameCurrentBranch?: typeof renameCurrentBranch;
+  localBranchExists?: typeof localBranchExists;
 }): Promise<AttemptFirstAgentBranchAutoNameResult> {
   const firstAgentContext = options.firstAgentContext;
   if (!firstAgentContext || !buildAgentBranchNameSeed(firstAgentContext)) {
@@ -129,15 +130,50 @@ export async function attemptFirstAgentBranchAutoName(options: {
     return { attempted: true, renamed: false, branchName: null };
   }
 
+  const localBranchExistsImpl = options.localBranchExists ?? localBranchExists;
+  const targetName = await findAvailableBranchName({
+    cwd: options.cwd,
+    desiredName: branchName,
+    placeholderBranchName,
+    localBranchExists: localBranchExistsImpl,
+  });
+  if (!targetName) {
+    return { attempted: true, renamed: false, branchName: null };
+  }
+
   const renameCurrentBranchImpl = options.renameCurrentBranch ?? renameCurrentBranch;
-  const renamedBranch = await renameCurrentBranchImpl(options.cwd, branchName);
+  const renamedBranch = await renameCurrentBranchImpl(options.cwd, targetName);
   return {
     attempted: true,
     renamed: true,
-    branchName: renamedBranch.currentBranch ?? branchName,
+    branchName: renamedBranch.currentBranch ?? targetName,
   };
 }
 
+const MAX_BRANCH_NAME_SUFFIX_ATTEMPTS = 50;
+
+async function findAvailableBranchName(options: {
+  cwd: string;
+  desiredName: string;
+  placeholderBranchName: string;
+  localBranchExists: (cwd: string, branchName: string) => Promise<boolean>;
+}): Promise<string | null> {
+  const { cwd, desiredName, placeholderBranchName } = options;
+  if (!(await options.localBranchExists(cwd, desiredName))) {
+    return desiredName;
+  }
+  for (let suffix = 2; suffix <= MAX_BRANCH_NAME_SUFFIX_ATTEMPTS; suffix++) {
+    const candidate = `${desiredName}-${suffix}`;
+    if (candidate === placeholderBranchName) {
+      continue;
+    }
+    if (!(await options.localBranchExists(cwd, candidate))) {
+      return candidate;
+    }
+  }
+  return null;
+}
+
 function maybeMarkFirstAgentBranchAutoNameEligible(options: {
   createdWorktree: Awaited<ReturnType<typeof createWorktreeCore>>;
 }): void {

packages/server/src/utils/checkout-git.ts

@@ -870,6 +870,10 @@ async function getWorktreePathForBranch(cwd: string, branchName: string): Promis
   }
 }
 
+export async function localBranchExists(cwd: string, branchName: string): Promise<boolean> {
+  return doesGitRefExist(cwd, `refs/heads/${branchName}`);
+}
+
 export async function renameCurrentBranch(
   cwd: string,
   newName: string,