'Press [F8]...' prompt does not show on the PXE booted client but menu works when F8 is pressed. In one case, prompt did appear normally when client was PXE booting with BIOS but not with UEFI.
The issue starts after boot menu items are added.
The length of everything in the menu is limited to 255 characters. This includes all the menu items, some additional data for each plus the actual 'Press [F8]...' prompt string with the server name added with default configuration. It is also worth noting that the 'Press [F8]...' prompt string is in the end of the transferred data.
The length calculation is not exact as the additional data varies a bit and there are differences in how that menu is retrieved and processed on the client side, for example the BIOS/UEFI difference.