LWC defaulting a checkbox input as checked based on a condition?

back again for some help.

I feel like this should be a really basic thing that I just can't seem to get to work.

I am loading some boolean values onclick of a button, and I'd like to default some checkboxes to checked if those are true.

Using

<template if:true={graValue}>
<lightning-input type="checkbox" label="(GRA)" onclick={handleEditRowSelection} value="GRA" checked ></lightning-input>
</template>

<template if:false={graValue}>
<lightning-input type="checkbox" label="(GRA)"  onclick={handleEditRowSelection} value="GRA"  ></lightning-input>
</template>   

handleEditUser(event) {
    this.graValue = event.target.dataset.gra;
    this.rimValue = event.target.dataset.rim;
}

 <lightning-button
variant="brand-outline"
icon-name="utility:preview"
label="Edit User"
name={user.Contact__c}
data-gra={user.GRA__c}
data-rim={user.RIM__c}

Always seems to default to true, even when the GRA value is false in the console log from that row button. I'm kinda at a loss as to what to do here.

Previously I tried setting the checked property on the input to be based on the value but am running into the same issue here.

When graValue = false, the checkbox is still displayed as checked even though the template should be rendering the unchecked one.

Any advice?