My advice to avoid confusion for such a sentence especially such a short sentence . Is avoid the possessive comm and the contraction. So that the reader knows exactly what you mean. This also avoids any misreading. "The toilet is clogged/blocked" blocked is far more common in British English. By putting in a contraction or a possessive comma. The sentence can be misunderstood in three ways. 1. Are three toilets clogged? 2. Is one toilet clogged. 3 Does the toilet possess/ have a glogged.

"The toilet is clogged" is a complete, correct English sentence. It is neither formal nor informal. "Toilet's clogged" is not strictly correct English. It is a shortening. When speaking informally, it is common to shorten things and leave words out. You can get from "The toilet is clogged" to "Toilet's clogged" in two steps. Step one is to replace "toilet is" with the contraction "toilet's," getting "The toilet's clogged." This is a correct English sentence. Now, we can leave out the word "the" because we can still understand the sentence without it. "Toilet's clogged" is no longer correct standard English. However, it's typical of the way people often talk in everyday life. But don't try to imitate this, it won't make it easier for English speakers to understand you.

A native English speaker would understand both sentences perfectly but, the first is more slang I suppose. Also, you would be more likely to hear the toilet is blocked/the toilet's blocked.

the second. or you could say "the toilet's clogged"

in very casual verbal conversation, yes, that is what you would hear. it's a short cut. technically not correct, grammatically. but it is what might be said.