fix(ai-client): re-evaluate continuation after chained tool approvals (#347)

* fix(ai-client): re-evaluate continuation after chained tool approvals

When a second tool approval arrives while a continuation stream is
already in progress, the checkForContinuation call is skipped due to
the continuationPending guard. This adds a continuationSkipped flag so
that, once the active stream finishes, the client re-checks whether
another continuation is needed, ensuring chained approval flows
complete correctly.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

* chore: add changeset for chained approval fix

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

* Approval flow documentation

* Small multiple approval fix

---------

Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>

Author: jherr

.changeset/chained-approvals-fix.md

@@ -0,0 +1,5 @@
+---
+'@tanstack/ai-client': patch
+---
+
+Fix chained tool approval flows where a second approval arriving during an active continuation stream was silently dropped