There are a couple parts to the question.
Can you cross the ceiling at all?
Any creature, climb speed or not, can potentially grab onto a ceiling feature and use it to cross a room. If the ceiling is covered in vines, carvings, rafters, or has some other potential handholds, it's up to the DM to determine whether the handholds can support your weight, and what roll (if any) is needed to maintain a grip and move across the surface hand-over-hand.
While most of the climbing rules talk about 'vertical' surfaces, it's pretty clear from our normal understanding of the world that an action like this would still constitute climbing and be subject to all the rules that relate to that, such as increased movement cost and requiring an Athletics roll if the surface is challenging. A climb speed operates as usual in this case, allowing you to ignore the movement cost increase.
(As examples, I would think that crossing from something like playground 'monkey bars' would not require a check, or only a minimal DC, while more difficult surfaces, such as a vine-covered ceiling or going from stalactite to stalactite, would be far more difficult.)
Can you climb across a smooth ceiling that lacks handholds or other similar features?
Probably not, unless the source of your climb speed (or some other rule) specifically says you can.
For example, the spider climb spell says
one willing creature you touch gains the ability to move up, down, and across vertical surfaces and upside down along ceilings
Similarly, the spiders in the Monster Manual share an ability called (again) Spider Climb, which reads:
The spider can climb difficult surfaces, including upside down on ceilings, without needing to make an ability check.
So ultimately, in your case, it depends.
A Simic Hybrid's climb speed is just a climb speed (it doesn't include a spider-climb clause), so it would not allow you to cross a ceiling without something to hold onto. But if there is something to grip and swing from (which is up to the DM), your climb speed could potentially allow you to cross a ceiling without slowing down. You may still have to make ability checks to climb on a difficult surface; a climb speed doesn't remove that requirement.