You are right, there is no one way to add a LAN device, like there is when pairing Zigbee or Z-Wave devices. So in my case, for things like my Logitech Harmony Hub, Philips Hue Bridge or my Kasa Smart Plugs, they all require a custom or built-in app that is written to specifically communicate with the device as there is no "standard" in the way there is for Z-devices (let's not get bogged down with the variety of standards adopted in Z-devices 
).
So for LAN devices you typically need some protocol / API a developer can call to establish a connection and communicate. This can be using UDP / TCP connections..... and this is where it gets outside my comfort zone... I'm more comfortable with those who have a REST API, which typically means cloud-based solutions.
Anyway, back to your main question... I'd suggest looking at the Device Compatibility List for those devices supported natively by HE, plus the list of Community-supported devices. Just because a device does not appear on these lists is not always a guarantee it won't be supported in some way, so it always pays to post here on the Community like you have. Plus there can sometimes intermediary systems that can help to open up control via HE. As an example, I have a Mousepad with an LED strip that can be controlled via local HTTP calls on my laptop, but not from outside, but I use EventGhost running on my laptop to provide something I can use to trigger adjustments in the mousepad from HE.
https://docs.hubitat.com/index.php?title=List_of_Compatible_Devices
