To Garfield, Pooky is more than VanPeltian security object. His psychology may be stunted, but Garfield prizes his individuality and selfhood to a degree that suggests he needs no transfer object to aid in separating himself from the One-ness of his mother (or, in this cat's case, a stand-in for his absent mother).
The teddy bear which Garfield has historically referred to as his "best friend," an object to which he speaks with more respect than his human and animal associates, is the sole recipient of Garfield's kindness, protectorship, compassion, warmth and unconditional love. Even the self-love with which Garfield regards himself is muddied with self-destruction, but what he gives to Pooky is unadulterated. In a way, Garfield funnels these feelings into this one-way relationship with Pooky making the teddy a strongbox repository for his soul.
In The Golden Bough, James Frazer catalogues extensive examples of the "external soul" motif in folktales from wide-ranging cultures, and extending back into the misty predawn of time. Magicians of myth hide their very mortality into remote, protected objects — in Inda, Punchkin conceals his vulnerability in a green parrot, and in Slavic folklore Koshchei the Deathless stashes his death in a hidden egg. Across time and continents, warriors of legend extract their sousl and lock them away before entering battle. In modern pop myth equivalent, compare to the Horcruxes in which Voldemort seals his sundered soul in Harry Potter, the jarred soul of the vampire warrior hero on Angel season 4.
In such stories the soul is detachable from its owner but they remain sympathetic. It is physical, has mass/ may be deposited elsewhere / takes the shape of an object. The irony of the "external soul" story is that in attempt to render himself invulnerable, the would-be immortal places himself at greater spiritual risk. First of all, the soul is extracted to facilitate ignoble or violent goals. Secondly, simply by existing, the immortal invites challengers to defeat him (and they invariably succeed). Finally, the immortal's fate becomes a matter not of his body's strength but his mental fortitude and virtue — his patience, modesty, tact, wisdom, etc. as he must keep the most vital of his secrets; this capacity is already symbolically hobbled by having removed the soul in the first place.
That Garfield pours his soul "into" Pooky is metaphorical, in the way that the bottle city of Kandor symbolically contains Superman's alienness as he protects his adopted home. But the cat empties his softer emotions upon the toy bear that he may sharpen his malice, coldness, and self-centeredness. It is as if Garfield acknowledges that every creature has the instinct to love, to express affection, to nurture, and the runoff is going to end up somewhere. Everybody's gonna need some kind of ventilator, and Garfield's is Pooky.
Jon Arbuckle could use cheering up on most days, and Garfield does not try to help. Odie's default setting is joy/ignorant bliss, and Garfield actively works to defuse that joy.
Upon the plush doll where he hides his heart, Garfield inscribes a parodic grimace of happiness.