dnd 5th – Can a creature with climbing speed break through the ceilings without penalty?

I do not know exactly what you are asking here.

Can you hang or cross the ceiling?

No matter which creature it climbs or does not speed up, it can potentially hang on a ceiling element and hang on it. If the ceiling is covered with vines, sculptures, rafters or other potential handles, it is the responsibility of the DM to determine whether the handles can support your weight and which roll (if any) is needed to maintain a grip and / or move on the hand-to-hand surface.

While most climbing rules speak of "vertical" surfaces, it is quite clear, according to our normal understanding of the world, that such an action would always be an escalation and would be subject to all the rules that relate to it, such as an increase in travel costs and requiring an athletic jet if the surface is difficult. In this case, the climb speed works normally, which allows you to ignore rising costs and not potentially roll.

(For example, I would think that moving from something like "monkey bars" on a playground would not require control, or only minimal DC, while much more difficult.)

Can you hang on or climb through a smooth ceiling that lacks handles or other similar features?

Probably not, unless the source of your climb speed (or other rule) specifically indicates that you can.

For example, the spider climb spell says

a willing creature you touch gains the ability to move up, down, and on vertical surfaces and upside down along the ceilings

Similarly, the spiders from Monster's manual share a capacity called (again) Spider Climb, which reads as follows:

The spider can climb on difficult surfaces, including upside down on ceilings, without having to perform capacity checks.

The climb speed of a Simic Hybrid (if I remember correctly) is simply a climb speed not including a clause similar to that of a spider, so it would not allow you to cross a ceiling without something to keep.