I have a gardenia, that I kept going now for over 20 years. It still doesn't look like much, but that is due to my errors over the years, it however is still alive, so I do have the horticulture down.
The above advice is good. Leave it alone until spring, then put it outside as soon as you are frost free. They are somewhat hardy, more a sub-tropical. They can take frost, and in the ground they are hardy through zone 8, a few cultivars are hardy into zone 7 in the ground. But I'm in zone 5, so they are a out in summer in for winter plant.
During winter I keep them as bright as I can indoors, though indoors, my under lights bright is at best equivalent to shade outdoors. I would not repot unless there is an obvious problem. Save repotting for spring, when it goes back outdoors. They are sturdy plants, in that mine has survived many episodes of neglect and less than ideal care. But they do die if you neglect them too much. Drying out totally is usually fatal. If your tap water is medium to very hard, meaning high in dissolved solids, usually the solids will be limestone. In this case you must use an acidic media and repot at least every other year. If your water is more like rain water, or RO water, you can get away with a less acidic soil. I will sift canadian peat moss, and add about 10% of the chunks that don't go through my fine screen, which is about the same as window screen. So my mix can contain up to about 10% peat. The rest is about 20% seedling size orchid bark, pumice, lava and kanuma. If you don't have kanuma, you can substitute more pumice. If you don't have pumice you can use perlite. Just perlite and peat moss was a mix I used in the past, it works, but the perlite is very light, shifts around too easily so is not good for small bonsai pots. It is okay for growing out containers.
If your gardenia was mine, I would move it to a larger nursery pot in spring, and keep it growing rapidly for the next couple years. During this time you would begin training. First you need to decide what you want. A single trunk? A multiple trunk? If you go single trunk, do you want a broom? Informal broom, or a single trunk line from roots to apex?
Then you need to identify the trunk line(s) you want to keep, identify branches to keep, branches to serve to thicken the trunk and branches that are excess. That will be enough work for the next 2 years. Don't cut anything off until towards the middle or end of this coming summer's growing season. Post pictures before you do and you can get help making these selections.
Nice, long term project tree.