Wired doorbell. Trying to connect to pre-existing one.

If you want a wired doorbell with video, Ring do one. For a simple wireless Bluetooth night vision, with speaker, doorbell push, none. The most basic with bells and whistles are twice the width and 50% taller. If you are going to invest in one, you may as well do it right. I just ordered one from wish.com

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Assumption, you are using a low voltage, wired doorbell. If you don't know, then call an electrician. (low voltage wire is not dangerous - however the transformer - which is usually wired into AC at your breaker panel - is dangerous, and you should shut off the breaker if you are working on that)
90% of the time it is the button at the front door.
First step, you should be able to unscrew the pushbutton at the door, to get at the wiring to the button switch. If you unscrew one of the 2 wires from the pushbutton and take it off does the chime stop? Then the problem is with the pushbutton.
If not, then there is either a short somewhere else in the wiring, or your chime itself has failed internally

https://www.home-repair-central.com/doorbell-wiring.html
https://www.thisoldhouse.com/how-to/how-to-fix-doorbell

You'll need to connect all the devices to your home's WiFi. But you don't say for sure if the doorbell is wired or not. You said 16 amps, but didn't say what voltage - is that transformer for the doorbell specifically? Once you have downloaded the Nest app to your phone, there should be a help video that can help walk you through the remaining steps. Also, you need to download the Google Home app to your phone to complete the setup.

See if there is sufficient voltage between the two wires using a voltmeter. Also check that there is voltage coming out of the doorbell transformer to the wires, and power from the regular AC line going into the transformer. Sometimes the transformer dies and it's time for a new doorbell, although in the old setups, the transformer was separate from the doorbell.

Home doorbells operate on a 24VAC transformer and cannot be wired to work with Lower voltage DC Video door Bells.

Connect the new wire to the wire going to the original door bell button. one core of the new wire to one core of the existing wire and connect the other new wire core to the other existing wire core. insulate the joints from each other and any metal surfaces.

pODUCT OVERviewThe IQ America Designer Series Wired/Wireless Door Chime features a glass and pewter cover for a contemporary look, and it can be used as a wireless or wired chime for your convenience.

• Big Ben 8-note, Big Ben 2-note, traditional 8-note, traditional 2-note, traditional 1-note, birthday song, Merry Christmas, Auld Lang Syne, Beethoven and U.S. national anthem sound options
• Up to 300 ft. wireless transmission range
• Adjustable volume control
• Wired or wireless design (wireless use requires a wireless push button, sold separately)
• Glass and pewter cover
• Easily add any IQ America wireless pushbutton (not included)
• Doorbell pushbutton not included
• MFG Model # : PC-5610
• MFG Part # : PC-5610

For the IQ America doorbell (mine is a DW2860), the diode that was packaged was a 1N4004. Search for it on eBay. They are very cheap.

We had a similar problem with a wired doorbell. There is a diode in the doorbell itself that causes the chime to ring fully. If the diode is backwards, you get just a small tone and can only hear the full chime if you hold the button down. If this sounds like your problem, open up the doorbell at the button end (or have an electrician do it) and reverse the diode.

yes it is very simple. All you have to do is connect either the two red wires together or the two black wires together and put the other remaining two on the doorbell chime to the common and front terminals. Here is how it works. One red wire leaves the transformer. It connects to the other red wire going to the pushbutton. When you press the button the voltage comes back to the bell on the black. You have the other black from the transformer on the bell so that completes the circuit. The only reason I say to put either the two blacks or two reds together is that way you're sure to have one wire from the transformer and one from the doorbell. Not a 'pair" of wires from each.