Half-tide doesn’t sound right to me, slack-tide is something else entirely, my google-fu has failed me.
stand of the tide’, which is when tide levels ‘stand’ at a maximum or minimum
Isn’t that when it’s just standing at high or low tide?
Some googling leads me to find it’s either “ebb tide” or “flood tide” depending on whether it’s halfway falling or halfway rising, respectively. I’m not sure if this is exactly half way though, some diagrams make it appear that any time in between in either one of these, not necessarily half way exactly.
We use them as just the tide flow here.
I wouldn’t be taken aback if someone said half tide, and is probably what I would use if I was asked on the spot