fix(webapp,sdk): keep chat.agent snapshots on one object store #6301

Job	Run time
Detect changes	4s
typecheck / typecheck	7m 20s
e2e-webapp / 🧪 E2E Tests: Webapp	3m 44s
sdk-compat / Deno Runtime	2m 13s
sdk-compat / Cloudflare Workers	2m 16s
sdk-compat / Node.js 20.20 (ubuntu-latest)	2m 14s
internal / 🧪 Unit Tests: Internal (4, 8)	6m 37s
internal / 🧪 Unit Tests: Internal (5, 8)	6m 31s
packages / 🧪 Unit Tests: Packages (1, 1)	10m 32s
sdk-compat / Bun Runtime	2m 17s
internal / 🧪 Unit Tests: Internal (1, 8)	7m 15s
internal / 🧪 Unit Tests: Internal (2, 8)	12m 12s
internal / 🧪 Unit Tests: Internal (6, 8)	6m 31s
webapp / 🧪 Unit Tests: Webapp (4, 8)	6m 54s
webapp / 🧪 Unit Tests: Webapp (2, 8)	3m 51s
webapp / 🧪 Unit Tests: Webapp (1, 8)	6m 14s
internal / 🧪 Unit Tests: Internal (8, 8)	2m 46s
sdk-compat / Node.js 22.12 (ubuntu-latest)	2m 9s
internal / 🧪 Unit Tests: Internal (7, 8)	6m 52s
webapp / 🧪 Unit Tests: Webapp (8, 8)	6m 29s
e2e / 🧪 CLI v3 tests (windows-latest - npm)	3m 40s
webapp / 🧪 Unit Tests: Webapp (6, 8)	9m 26s
webapp / 🧪 Unit Tests: Webapp (5, 8)	4m 45s
webapp / 🧪 Unit Tests: Webapp (7, 8)	5m 57s
e2e / 🧪 CLI v3 tests (ubuntu-latest - npm)	1m 52s
e2e / 🧪 CLI v3 tests (windows-latest - pnpm)	4m 30s
e2e / 🧪 CLI v3 tests (ubuntu-latest - pnpm)	1m 58s
internal / 🧪 Unit Tests: Internal (3, 8)	8m 45s
webapp / 🧪 Unit Tests: Webapp (3, 8)	3m 33s
webapp / 📊 Merge Reports	54s
packages / 📊 Merge Reports	27s
internal / 📊 Merge Reports	25s
All PR Checks	2s
	2h 31m 15s

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