Are there any website widget chatbots that offer conversation logs and analytics for support teams?

Yes — quite a few website widget chatbots include conversation logs, team inboxes, and analytics/reporting for support teams.

Common features to look for

• Conversation history / logs: full transcripts of chats
• Shared team inbox: agents can review and reply to conversations
• Analytics dashboards: response times, resolution rates, CSAT, volume trends
• Tagging and filters: to categorize issues and track patterns
• Agent performance metrics: workload, first response time, missed chats, etc.

Examples of tools that offer these

• Intercom – strong chat logs, team inbox, reporting, automation
• Zendesk Messaging – support-focused, good ticketing + analytics
• Freshchat / Freshdesk – chat widget with conversation tracking and reports
• Tidio – live chat + chatbot + basic analytics
• Crisp – shared inbox, chat transcripts, visitor info, analytics
• Drift – more sales-oriented, but has transcripts and reporting
• HubSpot Chat – conversation logs tied to CRM, basic analytics

If you want better support-team analytics, prioritize:

• Exportable transcripts
• Filters by agent, topic, and channel
• SLA/response-time reporting
• Integrations with help desk tools
• Role-based access and audit logs

If you want, I can also give you:

1. a comparison table of the best options, or
2. recommendations based on your team size and budget.