Some googling tells me that there are kits which retrofit a smart camera doorbell onto old school physical chimes, and that these can sometimes exhibit the problem you describe. The issue seems to be in that retrofit circuit somewhere. Example: https://community.ring.com/t/ring-pro-video-doorbell-delay-in-ringing-mechanical-doorbell/4045

Two sounds are emitted, according to that post:
Quote:
When the ring light around the button is off (dark) and the button is pressed, the Ring Pro device emits a sound immediately, BUT there is a delay of 3-5 seconds between pressing the button and the mechanical doorbell actually ringing.
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Tony Fabris