Don’t give up yet.
How many routers have you got connected, and what is connected to what? On top of that, what is hardwired to what, and what is connected to WiFi, and what router is offering up WiFi connections? What SSID’s are being advertised and what is connecting to what?
The router does routing (by design, duh!), sending traffic from one device to another, depending on how it is configured. We have to get the configuration correct so the paths are set up so the desired devices can talk to each other, which your HA Green did at one time, does not appear to be doing now, but most of the other devices are. One of the other functions it can do is allocated an IP when a device connects. It can be configured to do that in a fixed way (a static IP address that is consistent), or dynamically (pull a new one off the list available and give it out). Having multiple routers vying to do this in an uncontrollable manner can sometimes cause clashes.
I suspect we do not have the entire picture of your setup.
Some questions that come to mind:
Is your old ISP router still connected, acting as a router and trying to allocate IP addresses in DHCP mode? You mention putting your Starlink router into bypass mode, suggesting you may have a Gen2 one. If so, maybe you need to switch your Gen2 Starlink to passive mode to let the Gen 3 do the same without issues and conflicts, or plug the HA Green into the Gen 3 port? Why are you not switching the old Starlink router to passive mode? Does it still serve an useful purpose on the network?
How many routers do you need? Are any redundant? Are you still using them in the correct mode? Are you using the LAN connections on one as a switch because you do not have enough ports to connect the Ethernet cables on your Gen3, but have not changed the configuration to turn off routing?
Which router is the HA Green plugged into, the old ISP one or the new Gen3 one?
What make and model is the old ISP router?
Are the other devices hard wired or connected via WiFi?
Is there any network splitting or VLANs?
Are there any bridges, switches, hubs or other networking devices shuffling data around?
Yes, there are more questions.
These are questions that are part of getting everything to pleasantly chat together.
First things first
Before you start swapping things around more, lets get the big picture.
First, check your IP addresses for each router that is still powered on, your HomeAssistant device, and all the devices you are connecting to each.
What are the IP addresses of all the other devices on your network? How are they connected - hardwired or via WiFi? To what device?
Suggestion: I keep a network information spreadsheet with each device listed: one row for each device, and the columns for the name, the model number, serial number, the MAC address (doesn’t change), the IP address (can change, but I like to make them static addresses to prevent conflicts), the device it is connected to (it makes it easier if they have a primary one), how it is connected (Ethernet to what port, WiFi to what SSID), the SSID if advertising one, and any other relevant notes. You will find after about twenty devices you will need to do the same to keep track of everything.
List them here would be nice, and the penny will drop as to why the HA Green is not being seen.
Comment: Having multiple devices acting as routers can sometimes cause confusion - where do the data packets go? Having the possibility of devices connecting different WiFi SSIDs can sometimes also cause issues.
Security concern some people have when posting on the forum - what to redact? What to disclose?
Note, the IP addresses [192.16x.x.x ones] are local to your LAN and not directly accessible from the internet - they are behind a router - so don’t worry, there are no security implications in showing them to us. The SSIDs can be redacted, and can be called SSID1, SSID2, etc instead however to differentiate them for our troubleshooting purposes - just tell us which router is advertising which one, and what SSID the devices are connecting to). Passwords should always be redacted, even when it is suspected they may be mis-spelled as the cause of bad connections.
Routing does not need to be complicated. You don’t have to be a guru until you start to do sophisticated setups. Getting the connections right and what is configured as what is easier if you write it down, and the patterns will become obvious, and the ones that cannot connect will become evident.
Share the full network configuration and the suggestions will come in to solve your dilemma.