If I put all of my cameras (and also my BI machine I'm assuming?) on the same VLAN, how would I access it from my regular LAN?
For example, how would I remote into the server? Also how would I access UI3? What about my various camera feed integrations in Home Assistant?
VLANs can be hard to understand at first - or at least they don't operate how most beginners think they do. Most beginners (including myself) hear about VLANs and how the isolate and segment their network and assume the devices can never communicate between VLANs. This isn't how they work however. What really happens is that devices on a VLAN can't
initiate contact with devices outside of their VLAN (unless specifically set up to do so), but they can always
respond to requests from devices outside of their VLAN.
What this means is that you can isolate your cameras on their own VLAN and lock it down so they cannot initiate communication with devices outside of their camera VLAN (let's call it the CameraVLAN). However if you have the rest of your network set up on another VLAN (let's call it the MainVLAN) and you want to pull up the GUI of your BI/NVR machine (which is located in CameraVLAN) from a computer/phone/tablet/etc that is located on the MainVLAN, that won't be a problem if you have set the MainVLAN to be able to communicate with the CameraVLAN.
In that case, devices on the MainVLAN can "see" and communicate with ALL devices on the network including those on the CameraVLAN. However the devices on the CameraVLAN can only "see" the devices on the CameraVLAN and are "blind" to everything else. But just like a blind person can respond to someone speaking to them, the devices on the CameraVLAN can communicate with devices on the MainVLAN when the MainVLAN device starts the "conversation". But the devices on the CamaraVLAN are always "blind" to devices on MainVLAN, so as soon as the MainVLAN devices stops communicating with the CameraVLAN device, the CameraVLAN device doesn't even know the MainVLAN device exists anymore and can't communicate with it until something on the MainVLAN starts another conversation. Hopefully that makes sense.
In your case, as long as you set it up so that your MainVLAN can initiate communication with your CameraVLAN, all those devices you mentioned would work normally with regard to how they interact with the camera server. It would just "work". But the devices on the Camera VLAN would be isolated from the rest of your network and couldn't contact any of them or connect to the internet (assuming everything is set up correctly). This is why adding a VPN connection is the next step in the process too. So that once you have your VLANs set up, you can also set up a method to securely access your network while remote. Once connected to the VPN, you should have access to all your devices, including your cameras (assuming that is what you want and you set the VPN to access that VLAN. By default it's normal that the VPN would only allow communication with the MainVLAN, so you would need to add the CameraVLAN to the allowable connections over VPN).
This is a very basic explanation of how VLANs work (and it's probably wrong at a technical level), but it's how I began to understand it myself when I was first learning about it.