fix(ui): use categorical colors for tier donut, trim redundant turn count

[tin-berri]

Replaces SEQUENTIAL_COLOR_RAMP (blue monochrome gradient) with a categorical palette for the tier donut, increasing legend spacing for readability and removing the redundant turn count from the avg-saved-per-session metric (already shown in Routing by tier).

[greptile-apps]

Greptile Summary

The PR adds a per-router tier-routing donut with categorical colors and configured tier/model labels, while simplifying the savings summary by removing redundant turn totals.

• Adds tier-turn visualization and tests for complexity and quality router data.
• Loads auto-router deployment metadata to resolve custom labels and assigned models.
• Updates generated benchmark API typing and clarifies canonical complexity-tier casing.
• Reworks the savings hero card to emphasize average savings across sessions.

Confidence Score: 4/5

The PR appears safe to merge after the non-blocking repository-convention issue in the new test is cleaned up.

The tier visualization preserves router-group identity, safely handles absent configuration, and is well covered; the only accepted concern is prohibited explanatory commentary in the new test.

Files Needing Attention: ui/litellm-dashboard/src/app/(dashboard)/cost-optimization/_components/TierTurnsChart.test.tsx

Important Files Changed

Filename	Overview
ui/litellm-dashboard/src/app/(dashboard)/cost-optimization/_components/TierTurnsChart.tsx	Adds the tier donut, deployment-aware labels, and model annotations with safe fallbacks for missing configuration.
ui/litellm-dashboard/src/app/(dashboard)/cost-optimization/_components/TierTurnsChart.test.tsx	Thoroughly exercises chart labeling and configuration variants, but adds comments prohibited by repository convention.
ui/litellm-dashboard/src/app/(dashboard)/cost-optimization/_components/AutoRouterBenchmarksTab.tsx	Integrates router metadata and the tier chart while simplifying the savings and session summary layout.
ui/litellm-dashboard/src/app/(dashboard)/cost-optimization/_components/autoRouterBenchmarks.ts	Extends benchmark views to preserve group identity for group-specific tier visualization.
litellm/types/management_endpoints/auto_router_endpoints.py	Corrects the documented casing of canonical complexity-router tier keys.
ui/litellm-dashboard/src/lib/http/schema.d.ts	Regenerates the API schema to expose optional per-tier turn counts to typed UI consumers.

_{Reviews (1): Last reviewed commit: "fix(ui): use categorical colors for tier..." | Re-trigger Greptile}

[greptile-apps]

Remove prohibited test comments

These newly added comments violate the repository convention against adding source-code comments; the test name and assertions already communicate the scenario without them.

Suggested change

	view={groupView()} // complexity router
	autoRouters={[qualityDeployment] as AutoRouterDeployment[]}
	/>,
	);
	// No complexity_router_config on the quality deployment, so no tier labels are read,
	// falling back to canonical names. No models are shown (quality config doesn't have tiers).
	expect(screen.getByText("Simple 75%")).toBeInTheDocument();
	view={groupView()}
	autoRouters={[qualityDeployment] as AutoRouterDeployment[]}
	/>,
	);
	expect(screen.getByText("Simple 75%")).toBeInTheDocument();

Context Used: CLAUDE.md (source)

Note: If this suggestion doesn't match your team's coding style, reply to this and let me know. I'll remember it for next time!

[tin-berri]

Duplicate of #36291 (same branch, correct base: litellm_internal_staging). Consolidating there.