"The bottle is full of beer."
Translation:הבקבוק מלא בבירה.
It's a risky business, trying to translate prepositions word-by-word. Instead, think of the definition of a verb as including which prepositions go with it, and it is more or less arbitrary, although there are patterns. מילאתי את הבקבוק בבירה, הבקבוק מלא בבירה, because the verb למלא - to fill - takes a direct object which is the container, and an indirect object with a ב which is the content.
A bit more information about this, the verb does have another option where both the container and the content are without a preposition. מילאתי את הבקבוק בירה, הבקבוק מלא בירה, that is also correct. But של is nowhere on the definition of מלא.
I hope a native speaker helps with this question. I think it's a nominal sentence. The piel verb מלא would have another mem, correct? Here's a link to that binyan: https://www.pealim.com/dict/1053-lemale/ The adj. מלא takes ב. The reason there is no copula is that there are two nouns (הבקבוק and בירה). Does the pa'al binyan of this verb have a passive? https://www.pealim.com/dict/2701-limlot/ But the adj. is, as you indicate, מָלֵא.