@ScarlettJ
Has your Google Nest Hello Doorbell been unused since you bought it in April 2021?
I'm asking because the Nest Hello has a small internal battery whose primary purpose is to provide power for the doorbell's camera during the instant when the doorbell button is pressed and power is diverted to ring the internal doorbell chime. However, I THINK that battery is also used to provide power to the doorbell during initial setup. If your doorbell has not been connected to power for almost 3 years, maybe that internal battery is drained.
I can't remember whether the Nest Hello comes with a USB-C cable, but you could try connecting it to a USB charger for awhile, or connecting it to your doorbell wires for a couple of days, to see if this charges the battery, and then try to install it.
When you did the factory reset, did your doorbell chime and its light ring start spinning blue, and flash yellow, and them chime and the light ring start pulsing blue, as described in the factory reset instructions (NOT the "restart" instructions)? (https://support.google.com/googlenest/answer/9252162). If you didn't get any lights, maybe that's an indication the internal battery is drained.
I'm guessing on some of this; there's not much documentation on it.
By the way, there is also a known defect that causes the internal battery on the Nest Hello to fail after a year or two. It's failed on two of our three Nest Hellos. The chief symptom is that the doorbell goes offline for a minute whenever the doorbell button is pressed. The workaround is to turn off the "Indoor chime" option so the doorbell no longer tries to ring the indoor doorbell chime, and rely instead on the "Visitor announcements" option (https://support.google.com/googlenest/answer/7672451). I don't know whether this internal battery could fail if a doorbell is simply not used for 3 years.
