Chiming in, since I recently had the same problem with HC Classic on Soulseeker.
First of all, since I don’t seem to have the necessary “trust level” here to include links in my post (I don’t visit the forum very often, despite having the same WoW account since 2004), I will have to resort to base64 encoded links. I will mark the links via “(base64 link)”.
If you want to decode/visit a link below, you will first have to Google “base64 decoder”, visit the website and decode my link there. I’m truly sorry for that, but since my post requires links, I currently see no other way around it 
Back to topic: An example how my disconnects look like can be seen here (base64 link): aHR0cHM6Ly95b3V0dWJlLmNvbS93YXRjaD92PW1CTlFybnU0UFow
In my case, first the chat cuts out (I can’t write anymore in group or guild chat, several seconds later the whole connection breaks down). The frequency of disonnects varied - sometimes it would disconnect me 30 seconds directly after logging in, sometimes I could play for some hours before experiencing the issue.
I also opened a ticket regarding the issue and the GM directed me to this thread in the US forums (base64 link):
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They are investigating an issue with frequent disconnects on US HC Doomhowl and apparently fixed or mitigated it on the US PTR HC realm.
Despite this development I decided to have a closer look at my own diconnects and analyzed the WoW traffic when the diconnects are happening (I’m an IT guy).
Turns out that there is/was a problem with the so-called PMTU discovery. Without going into too much detail, the (P)MTU ((path) maximum transfer unit) is a variable that determines the largest possible size of a datagram being sent between two communication partners. The size may vary depending on the hops packets are passing on their way and on protocol encapsulation (like PPPoE for example).
The automatic adjustment of the (P)MTU for a connection is called PMTU discovery. In my case there was a problem with this mechanism. I implemented a fix/workaround on my router and since then the disconnects stopped.
Since network problem sources can vary considerably, it is very possible that your problems are not related to my issue at all and that the fix being worked on is for another issue causing the same symptoms.
But there is a way to test this: You could (temporarily) lower the MTU of your PC running WoW and then check, if the problem still persists.
Disclaimer: Lowering the MTU is harmless and can be reverted easily, but may have side effects (like a slightly lower network performance). If you decide to do so, it is on your own risk.
That being said: If you want to test this, you can try to lower your MTU from the default 1500 to something like 1420, which should be low enough so that PMTU is not needed at all, which would elimate PMTU discovery as the source of the disconnect problem.
To accomplish this, you can follow the description here (base64 link):
aHR0cHM6Ly93d3cud2lzZWNsZWFuZXIuY29tL3RoaW5rLXRhbmsvNjcwLUhvdy10by1DaGFuZ2UtTVRVLW9uLVdpbmRvd3MtMTEuaHRtbA==
, section " How to Change the MTU on Windows 11" and set the MTU to 1420 on your primary network interface.
Of course you can also follow any other guide describing how to set the MTU in Windows 10/11.
Afterwards, you will have to restart Battle net and your WoW client to check, if the problem is gone.
To revert to the default MTU size of 1500, simply follow the same steps as above and set it back to 1500.
As already stated above: It is possible that your problem is not related to my problem at all and that the test will fail and the disconnects persist. In this case you will probably have to wait for Blizzard to deploy the US PTR fixes to the european live servers.
Cheers
Edit: The US HC PTR fix has apperently been deployed to all live realms now, so check first, if the problem has been solved by the Blizzard mitigation