For example, when I long press on a hyperlink, the context menu shows, but the hyperlink opens right after I stop pressing. See this video:

It seems that long press actually performs both left and right click.
The device I uses is wacom's tablet.
I have this as well, my solution is to slightly drag off the link while holding the long press and then let go, and click my choice in the rt click menu.
> I am facing the problem that the context menu immidiately disappears after popping up. Seems like this is the issue.
I have the same issue on XFCE4/Alpine Linux :)
I added most of the fixes I could find and for this issue I added grabbing
the events and filtering out the left-click that happens during a right-click.
I'm running an rPI-CM5 with Wayland and a 6.6.x kernel with a Waveshare
LCD /Touchscreen.
Check my repo here is you'd like to try it:
https://github.com/n1gp/evdev-right-click-emulation
We develop alternative right click solution
https://github.com/pardus/eta-right-click
It has event filter and simple configuration gui
<img width="408" height="394" alt="Image" src="https://github.com/user-attachments/assets/df3b80ab-4cef-4c05-95dd-f1bf40cc4c71" />