I've never seen anything that can do all that in one unit...
You can get all the bits individually, to work via Ethernet.
You would need a WiFi link to start with. A pair of TP-Link CPE-510 APs would give you that:
https://www.amazon.com/TP-Link-300Mbps-dual-polarized-directional-CPE510/dp/B00N2RO63U
Then, probably a SIP-based (VoIP) door entry unit.
They allow communications over a network to anywhere. You use another SIP compatible device (or a home telephone system if that is also SIP compatible) and the door entry unit just calls the phone number of whatever device you program it for - a single phone or a ring group on an exchange.
eg, just for some examples:
https://www.provu.co.uk/door_entry.html
The entry phone usually also has a relay contact output to remotely trigger a door or gate release.
Some include a webcam so you can see who is at the door/gate before releasing it.
With Ethernet, you can also add other IP cameras where you need them, just connect a small ethernet switch to the gate-end WiFi AP to get as many ethernet connections as you need.