I haven't stumbled upon anything officially called 'Cozy Obsession' as a published novel title, so you might be thinking of a web novel or a story on a serial platform. If it's a webnovel, the big sites are your starting point. I'd check Wattpad, Royal Road, and Webnovel directly. Their search functions can be finicky, so try variations like 'cozy' and 'obsession' separately, or think about related tags—'low-stakes fantasy', 'slice of life', 'comfort read'. Those tags often house the vibe you're after.
Sometimes these stories get renamed or are part of a larger series, which makes tracking them down a real chore. I once spent an hour looking for a story I'd only half-remembered, only to find it had been taken down for a rewrite. If the usual suspects don't turn it up, maybe ask in niche subreddits or Discord servers dedicated to cozy reads. Readers there have encyclopedic knowledge of the smaller, lesser-known serials. A lot of writers start on one platform and then jump to another, or pull their work to publish on Amazon Kindle Unlimited, so that's another place to glance at, even if you're looking for a free read initially.
If you do find it, the 'obsession' part of the title in a 'cozy' wrapper sounds like it could be a fun twist—maybe a gentle, domestic fantasy where the protagonist's obsession is something harmless like perfecting a bakery recipe or cultivating magical herbs, rather than a dark romantic trope. That specific blend can be really hard to locate, but when you find it, it feels like discovering a secret garden.