feat(ai, ai-client): add SessionAdapter for durable session support.

.changeset/tidy-zebras-drum.md

@@ -0,0 +1,12 @@
+---
+'@tanstack/ai': patch
+'@tanstack/ai-client': patch
+'@tanstack/ai-react': patch
+'@tanstack/ai-solid': patch
+'@tanstack/ai-svelte': patch
+'@tanstack/ai-vue': patch
+---
+
+Add durable `subscribe()`/`send()` transport support to `ChatClient` while preserving compatibility with existing `connect()` adapters. This also introduces shared generation clients for one-shot streaming tasks and updates the framework wrappers to use the new generation transport APIs.
+
+Improve core stream processing to better handle concurrent runs and resumed streams so shared sessions stay consistent during reconnects and overlapping generations.