fix(models): keep ordinary chat selections session-scoped (#139232)

fix(models): keep ordinary chat selections session-scoped (#139232)

Keep ordinary model choices in their session, including administrator choices. Preserve explicit agent/global scope and the shipped SDK persistence opt-in, resolving its write target inside the current config transaction.

Real Gateway red/green, selected-model chat continuation through the bundled provider, focused regression coverage, independent review and exact-head CI cover the extraction from #136257.

Co-authored-by: Ayaan Zaidi