I am having the same issue.
My world started on Java 1.19.4
I am running Fedeora Linux running Open Java 17.0.3 64 bit.
My cpu is an AMD R5 3600.
My video card is NVIDIA Geforce RTX 2070 Super.
I have increased the ram from 2Gb to 4Gb in the launcher. I have also disabled the F3 screen in the create world menu. Other than that, everything is vanilla.
I get the feeling that it is just creating the second portal over the first. Unfortunately, it goes to the same island as the first one.
I should add that I tried killing the dragon with beds the first time. So there is an obsidian block 1 block off the center and 1 block up from the post of the dragons perch.
[Edit]
I have decided to remove the obsidian block by the perch. Gave my self 4 end crystals, summoned the dragon, and used the kill command to kill the dragon, /kill @e[type=minecraft:ender_dragon] and the end gateway appeared.
[Edit 2] I gave myself 4 more crystals and beat the dragon manually, but no obsidian block by the perch. A third gateway now appears.
This is happening again in 1.16.3. I literally cannot catch them except when casting.
I am running an r5-3600 with EVGA Gerofrce RTX 2070 Super.
I have other raid bugs as well. I will search for the corresponding tickets. I think raids are broken.
I recently was able to reproduce this in a warped forest in the nether.
MC-273708 does seem related, but in my case the enderman attacks me.
I was running 1.21.4 on standard survival.
I also found that if I ran away the teleporting around me continued along with the attacks.
It is as if the enderman was like an invisible ninja around me doing constant attacks. If I stopped moving I died. Eventually, the enderman would suffocate and the attacks would stop.
Edit: I realized I should give more info.
I only looked at the enderman and lured into the boat specifically to suffocate it. I didn't need to attack it to be attacked.
Also, I am running Fedora KDE Plasma with X11. Hope this helps.