Glad you got there, and it is worth having the answer written down on the thread. For anyone finding this later, the setting that mattered is a Start11 one rather than a Windhawk one: Taskbar > Show seconds on the taskbar clock = Off.
Since you are deliberately running Start11 alongside a third-party taskbar tool, there is a documented key for that arrangement that goes further than the UI toggle. In HKEY_CURRENT_USER\SOFTWARE\Stardock\Start8\Start8.ini\Start8, add a string value (REG_SZ, not DWORD) named S11_BLOCKMOSTTASK set to 1.
It is documented as stopping Start11 from modifying most taskbar behaviour for compatibility with third-party tools, and it turns off the enhanced taskbar, taskbar colour control and the custom start button along with it. It needs an Explorer restart to take effect, not just a settings reload, and it leaves the Start menu alone. It arrived in 2.7.0.1, so your 2.74 has it.
I would not put it forward as the answer to the seconds behaviour. You already have that solved, and the key is not documented against the clock specifically. It is the one to reach for if any other Start11 and Windhawk overlap shows up on 23H2.
The full key list, with the version each one was added in, is here: https://support.stardock.com/space/SHC/1750138994