Six front doors into the practice, and nobody owns the web chat
Count the ways a patient can reach you, then name the person responsible for each one.
A typical practice has more inbound channels than it realizes: the main phone, the web form, the Google Business Profile message thread, a chat widget, text messages to a tracking number, referrals from other offices, and people who walk in from the block. Most practices staff two of those properly.
Do the inventory on paper. For each channel: who watches it, how fast, what happens after hours, and where the record ends up. Any channel without a name next to it is a leak, and the unread ones are usually chat and profile messages.
Turn off what you cannot staff. A chat widget that collects inquiries nobody answers until Monday is worse than no widget, because the patient believes they have made contact. Same with a contact form that routes to an inbox one person checks on Fridays.
Then set a response clock. Inquiries decay quickly in dentistry, especially anything urgent, and the practice that replies first usually gets the patient regardless of who is better.