I’m sorry not really an object person (as in, unless there’s a specific reason I wouldn’t ship a character with an object. I do find shoving objects in holes to be a bit sexy). I tend to like sentience (so Eyelander would be a go) OR if it is an object it’d have to be personified (Like Heavy’s minigun Sasha). However! I’m still here to answer this question

Soldier x Bucket is based (mostly) on his time in Expiration date. This could be particularly compelling as he specfically asks for it. Yet, the bucket doesn’t do to much for him. This is extremely one sided, with Soldier desiring the bucket and the bucket is… just a bucket. Now, he may put the bucket on his head! He could carry things around in the bucket! Alas, though, this seems very fleeting to me.

Soldier x Shovel on the other hand… that’s his weapon! He is known to have it on his person! This is a trusty and reliable tool! However, a replaceable one. Oh woe! He gets a board with nails in it and now that’s his mele weapon…

I will say shovel, for now, but my mind could be swayed.

Also hello to the four people who follow me! I’m answering stuffs again