With the exception of the Dieppe raid (19 Aug 1942) between June of 1940 when the Germans captured northern France and June 1944 when the D-Day invasion took place there was essentially no ground combat on the channel front. Combat was in the air or from the air to the ground, and some naval skirmishes with the notable exception of the "Channel Dash" (11 Feb 1942).
Very few of the experienced front line troops defended the coast, their experience and skills were needed elsewhere.
Even on the eve of the invasion few front line troops were defending the beaches, the bulk of them were being held further inland (safe from naval gunfire) the idea being they would be moved to the beaches when it was clear exactly where the landings were taking place.
For numerous reasons (including Allied air superiority) that didn't work as well as the Germans had hoped it would.
Quite a bit of the wooden bullet training ammo was found in German bunkers as the Allies landed and moved inland, and its likely at least a few round of that stuff was fired at the Allies, but that wasn't what it was there for.
The idea that the Germans made wooden bullets to cause greater wounds was just a made up rumor, something that sound plausible (though inaccurate) to explain why it was there, and in the process further vilify the enemy for their cruel and wicked ammo.
I do not know if the Japanese used any wooden bullet training ammo, or not, but have heard numerous stories about Japanese "Bamboo bullet". Never saw any proof they existed, but lots of GI were convinced they were a real thing.
It is remotely possible that some Dutch wooden bullet training ammo was captured by the Japanese when they took Java and the rest of the Dutch East Indies, and that stuff (in Japanese hands) MIGHT have been the origin of the "Bamboo bullet" stories, no one can say for sure.