Pulling to one side doesn't automatically mean your suspension is shot, but it does mean something needs attention - and soon, since it's been going on for a month. The most common culprit is actually a wheel alignment issue rather than broken suspension components. A 2023 Civic shouldn't have worn-out suspension parts yet, so you're probably looking at either misaligned wheels (which shifts the steering wheel off-center) or something like uneven tire pressure, a stuck brake caliper, or worn brake pads on one side.
Start by checking your tire pressure on all four wheels with a proper gauge - low pressure on one side can absolutely cause this. Then get an alignment check at a shop; it's usually cheap or free, and they'll tell you immediately if the angles are off. If alignment looks fine, have them inspect your brake system and suspension components for wear or damage. The fact that you haven't hit anything major is actually good news - it suggests gradual wear rather than impact damage, which is typically easier and less expensive to fix.
Don't ignore it though, because pulling to one side puts uneven stress on your tires and suspension over time, which can make problems compound. A proper diagnosis takes maybe an hour at a shop, so get it checked before the issue gets worse.