docs(tools): add OAuth Connect popup troubleshooting to Google Calendar/Sheets

[Mehayla]

What changed

Added a Troubleshooting section to two existing integration pages:

• fern/tools/google-calendar.mdx
• fern/tools/google-sheets.mdx

Each new section covers: "Connect button doesn't open the Google authorization popup", with a numbered checklist (check browser console for a Nango-related CSP error, allow pop-ups, disable ad blockers/privacy extensions, allow third-party cookies, try Incognito/another browser, allow *.nango.dev on managed networks), plus what to include when contacting support if it's still unresolved. The Google Calendar page also gets a short note on using a Custom Tool with a manually-supplied OAuth token as an alternative when the built-in Connect flow isn't viable.

No other content on either page was modified.

[Mehayla]

Why this change

Gap type: Incomplete content — both pages document the happy-path Connect flow but have zero troubleshooting content for a failure mode that is currently the single largest recurring support driver in the help-center feedback review.

Evidence (rolling customer-feedback review via Enterpret, support tickets + Ask AI chat + Discord):

• 76 distinct customer conversations in the trailing 4 weeks explicitly describe the Google Calendar/Sheets "Connect" button failing to open the Google OAuth popup, spread across every week in that window (not a one-off spike/incident) — e.g. tickets on Aug 3, 4, 5, 6, 7, 9, 24, 25 all report the identical symptom independently.
• Recurring, specific details confirmed across many of these tickets: the modal closes/redirects with no OAuth window; browser console shows a Content Security Policy violation blocking an inline script from connect.nango.dev / api.nango.dev; some users additionally hit Missing Nango configuration for tool type: google.calendar.availability.check when they try to use the tool anyway.
• Customers report trying the standard fixes themselves (allowing pop-ups, Incognito mode, different browsers/devices, disabling extensions) before filing a ticket, and support has no documented checklist to point them to — each ticket currently gets handled ad hoc.
• Checked docs.vapi.ai/tools/google-calendar and docs.vapi.ai/tools/google-sheets (Step 1 "Connect" instructions) and docs.vapi.ai/faq — none mention this failure mode, the CSP/Nango error, or any workaround.
• One Ask AI conversation shows the assistant improvising a workaround (custom HTTP tool with a manually supplied OAuth token) because there's no documented alternative path — that's now captured as a documented option on the Calendar page instead of being reinvented per conversation.

Why docs now, regardless of the underlying fix: whether or not the root cause is a Vapi-side CSP/Nango bug, a documented checklist lets customers self-serve the common causes (extensions, third-party cookies, corporate network policy) and gives support a consistent diagnostic ask (console error text + browser/OS + Incognito repro) instead of every ticket starting from zero. It should reduce ticket volume and time-to-resolution immediately, independent of any product-side fix timeline.

Ranking: This topic had the highest current-week volume among substantive (non-generic) topics and was persistent across the trailing 4 weeks, so it was picked over other recurring-but-declining topics (e.g. phone number setup, outbound calling API errors, SIP trunk transfer errors) per the top-gap selection method.