Based to the description of both the feat and the spell the dice used for the attack is a d8, the language used is extremely specific and after reading it carefully you can notice how the two description match perfecly.
My best bet is that Crawford misread Polearm Master (the d4 is called specifically "weapon damage die" as in the description of shillelagh, he believed it was written just as "damage die"; In that case the dice used for the attack would be a d4 and no wander, it's really easy to miss, I had to check it more than once to be sure myself).
All the more the interaction becomes really confusing in practice: how exacly should shillelagh work, just some attack do damage from the magical aura of the spell? The enchantment is weaker based on the way you attack? Or some part of the staff are just not affected?
If they think it's right to use a d4 it's really fine, it barely makes a change (a sad ~1.5 dpr increase in a combat, in the rare occasion you are using both the action and bonus action to attack), and if so they should really make an errata and change the text of the feat and especially explain how the interaction work in practice in game.
For now the manual is clear on using the d8 and for me it makes way more sense practically but if you want to use this interaction, talk to your DM before the session and in the end it's not a big deal, flavour the spell as you like and have fun with it regardless of the dice used.
p.s.: nobody in the right mind would use this on a druid in a challenging campaign, their actions are way too valuable already and going melee is too risky for concentration, the only way this can be an interesting option seem to be a 'SAD' Ranger meme build but it's way far from the optimized standard of damage