Website Chatbot & 24/7 Live Chat setup (or other system)

I need a conversational bot setup and embedded directly on my website that can
1) take customer details and answer our most common FAQs,
2) assist visitors with everyday basic customer-service issues, and
3) collect brand-new enquiries and push them into our CRM with information such as visitor path eg google.com, page history.

The bot should stay online around the clock. During normal office hours any conversation that needs a human touch must transfer smoothly to a live-chat window so my support team can pick it up without the visitor noticing a break in the flow. Outside those hours the bot should handle the entire exchange, set expectations, and create a ticket

I’m open to whatever works, but have been looking at live chat / chatbot so far. A requirement is to be able to track user path and referral from google / fb etc

Deliverables:
• Discovery call to confirm user journeys, FAQs, and escalation rules
• Bot conversation flows, trained intents, and fallback responses
• Integration and on-page widget installation with our existing site
• Live-chat operator panel with clear instructions for my team
• Some testing and refinements before we go live
• Some training and a short hand-off video or document so we can maintain the bot ourselves

If you’ve set up similar 24/7 website bots with human handover, please tell me what platform you prefer and share a quick example.