
Reolink
Wired Video Doorbell Series
No subscription, local storage, HA-friendly; no mechanical chime.

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I would recommend the Reolink doorbell (not battery). There is also the Amcrest AD410, but most have jumped onto the Reolink once it was released. Reason being is it isn't locked down, you can add it other NVRs, software (i.e. Blue Iris), or your own NVR stack (Scrypted NVR - AI face recognition etc). All your own storage. Not that expensive to do imo- mini PC $180 + NAS/external storage $250.
Its more than your budget, but I have the Amcrest 4MP. It ticks all the other boxes though.
One thing to note with using this in Frigate. If you use the two-way URL, it will prevent the doorbell button from working. The cameras are a little stupid in this regard. What I did was add both the two-way and one-way URLs to the Frigate go2rtc section but only added the one-way URL to the camera config. You can then add the two-way feed to your HA frontend and it will only load it when you select that tab. I chose this camera specifically because of its size. I don't have enough room for most smart doorbells and only this and the OG Nest wired doorbell would fit - and even still, I have to use the angled pieces to keep it from banging against my storm door.
I have a Amcrest AD410 that has been a great unit and requires a "key" pin to release it from the wall. It's pretty solid on there I have struggled to get it off even with the key. They are a hard device to come by right now though. The manufacturer website still lists it as an available model but it has been out of stock for awhile. Maybe eBay or similar. 🤷
I have been using the Amcrest AD410. Initial setup requires cloud, then you move to your VLAN internal and it hooks up seamlessly to Frigate, etc. I have 3 issues and would not recommend this: 1. Initial setup requires phoning home. Makes it a hassle to reconfigure. 2. Known issue where battery swells (they have a small battery). Amcrest warranty is great and has replaced mine but it's unfortunate this happens and you have to go without a doorbell for 2 weeks or so waiting on a replacement. Then see point #1 when you get it. 3. When the power goes out the device comes backonline flahing a big green ring. IMHO, this is a serious design flaw as it signals the doorbell has issues. It's visual only - the camera works fine - but I sure wish there was a less obvious "this doorbell has issues" signal. The green green flashing just means it can not connect to the Internet. There is a way to 'curl' the doorbell via IP and disable it but what a hack! I do not plan to use this one again. Wanted to share my experience.
Ubiquiti G4 Pro WiFi if you have any UBNT gear already. The Amcrest 4MP doorbell fits the bill by supporting RTSP which you can easily capture on your NAS. https://amcrest.com/4mp-wifi-camera-doorbell-ad410.html Reolink Video Doorbell WiFi supports RTSP as well. https://m.reolink.com/us/product/reolink-video-doorbell-wifi/

Reolink
Wired Video Doorbell Series
No subscription, local storage, HA-friendly; no mechanical chime.

Ubiquiti
Doorbell Lite (UVC-Doorbell-B)
Affordable Ubiquiti; reliable; requires ecosystem; quiet chime.

Aqara
Smart Video Doorbell G4
HomeKit native; flexible power; poor battery life; narrow view.

Ubiquiti
G4 Doorbell Pro (UVC-G4 Doorbell Pro)
Premium Ubiquiti; advanced features; requires ecosystem hardware.

eufy Security
Video Doorbell E340
Dual cameras, strong privacy; slow app, poor battery.

Ranked #1
Reolink - Wired Video Doorbell Series

Ranked #1
Reolink - Wired Video Doorbell Series

Ranked #1
Reolink - Wired Video Doorbell Series

Ranked #1
Reolink - Wired Video Doorbell Series

Ranked #1
Reolink - Wired Video Doorbell Series