Dynamic cooldown + modal not working as expected in disnake

Question

I'm using a button to send a modal. I want there to be a cooldown that prevents people from spamming the button. I added a cooldown that works almost as intended, but the cooldown only gets triggered when I hit "cancel" on the modal. When I submit the modal, the cooldown is not triggered, and I can spam it as many times as I want. This is the opposite of what I want, I don't want the cooldown to be triggered if the user changes their mind and cancels the modal. I do want it to trigger when they actually submit it. Here's the View:

class MyView(disnake.ui.View):

    def __init__(self):
        super().__init__()
        self._buckets = commands.DynamicCooldownMapping(thread_cooldown, commands.BucketType.user)

    async def interaction_check(self, inter: disnake.MessageInteraction) -> bool:
        current = inter.created_at.replace(tzinfo=datetime.timezone.utc).timestamp()
        bucket = self._buckets.get_bucket(inter, current)  # type: ignore
        if bucket is not None and (retry_after := bucket.update_rate_limit(current)):
            await inter.response.send_message(f"You are on cooldown for another {retry_after:.0f} seconds.")
            return False  # on cooldown!
        return True  # good to go!

    @disnake.ui.button(label="Please work")
    async def cooldown_button(self, btn: disnake.ui.Button, inter: disnake.MessageInteraction):
        await inter.response.send_modal(modal=threadModal())

and here's the modal:

class threadModal(Modal):
    def __init__(self, forum):
        self.forum = forum
        components = [
            TextInput(
                label="Title", 
                max_length=100, 
                placeholder="Choose a title for your thread", 
                custom_id="title"
            ),
            TextInput(
                label="Description",
                placeholder="What is your thread about?",
                custom_id="description"
            ),
        ]
        super().__init__(title="New Thread", components=components)

    async def callback(self, inter):
        if self.forum == None:
            return
        if self.forum == "button":
            self.forum = inter.channel
            try:
                await inter.response.send_message()
            except:
                pass
        else:
            embed = disnake.Embed(
            description=f"Thread created in {self.forum.mention}.",
            color=0xFF5733,
            )
            await inter.response.send_message(embed=embed, ephemeral=True)
        embed = disnake.Embed(
        title=inter.text_values["title"],
        description=inter.text_values["description"],
        color=0xFF5733,
        )
        embed.set_author(name=f"Thread created by {inter.author}", icon_url=inter.author.display_avatar)
        message = await self.forum.send(embed=embed, view=MyView())
        await message.create_thread(name=inter.text_values["title"])

Thank you!