fix(webapp,sdk): keep chat.agent snapshots on one object store #6298

Job	Run time
Detect changes	3s
e2e-webapp / 🧪 E2E Tests: Webapp	3m 20s
packages / 🧪 Unit Tests: Packages (1, 1)	10m 8s
typecheck / typecheck	7m 11s
sdk-compat / Deno Runtime	1m 59s
e2e / 🧪 CLI v3 tests (ubuntu-latest - npm)	1m 57s
e2e / 🧪 CLI v3 tests (ubuntu-latest - pnpm)	1m 57s
sdk-compat / Bun Runtime	2m 12s
e2e / 🧪 CLI v3 tests (windows-latest - npm)	3m 36s
sdk-compat / Cloudflare Workers	2m 36s
e2e / 🧪 CLI v3 tests (windows-latest - pnpm)	4m 17s
webapp / 🧪 Unit Tests: Webapp (1, 8)	6m 39s
sdk-compat / Node.js 22.12 (ubuntu-latest)	2m 11s
internal / 🧪 Unit Tests: Internal (4, 8)	7m 2s
internal / 🧪 Unit Tests: Internal (2, 8)	7m 0s
webapp / 🧪 Unit Tests: Webapp (4, 8)	7m 6s
internal / 🧪 Unit Tests: Internal (3, 8)	6m 59s
webapp / 🧪 Unit Tests: Webapp (5, 8)	5m 8s
sdk-compat / Node.js 20.20 (ubuntu-latest)	2m 8s
webapp / 🧪 Unit Tests: Webapp (8, 8)	6m 25s
internal / 🧪 Unit Tests: Internal (7, 8)	6m 54s
webapp / 🧪 Unit Tests: Webapp (3, 8)	3m 10s
webapp / 🧪 Unit Tests: Webapp (2, 8)	4m 31s
webapp / 🧪 Unit Tests: Webapp (6, 8)	8m 10s
internal / 🧪 Unit Tests: Internal (1, 8)	6m 43s
webapp / 🧪 Unit Tests: Webapp (7, 8)	5m 47s
internal / 🧪 Unit Tests: Internal (8, 8)	2m 41s
internal / 🧪 Unit Tests: Internal (5, 8)	5m 49s
internal / 🧪 Unit Tests: Internal (6, 8)	6m 44s
internal / 📊 Merge Reports	28s
webapp / 📊 Merge Reports	49s
All PR Checks	2s
packages / 📊 Merge Reports	1s
	2h 21m 43s

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