General American has the "cot~caught merger", which means that the RP phonemes /ɔ/ and /ɒ/ are no longer distinguished. As a result, "cot" and "caught" are pronounced the same. (The "father~bother merger" also merges in /ɑ/.)

As a result, most dictionaries will either use whichever phoneme is found in non-merging dialects (to make their dictionary more useful outside of America), or apply one or the other consistently across the board. As a speaker with the merger, I tend to use ɔ in broad transcriptions, simply because it's easier to type on my IPA keyboard. Or, if I'm also representing the father~bother merger, I'll use ɑ, since it's the most peripheral of these vowels.

As to the exact pronunciation, it'll vary a lot, even within "General American"—a surprising amount of variation can fit under that label! Since there's no longer a distinction there, a certain speaker of a certain word might use something closer to [ɔ], or something closer to [ɒ], without it making a difference.

The dialect that your dictionary refers to as "General American" has the "cot~caught merger", which means that the RP phonemes /ɔ/ and /ɒ/ are no longer distinguished. As a result, "cot" and "caught" are pronounced the same. (The "father~bother merger" also merges in /ɑ/.)

As a result, most dictionaries will either use whichever phoneme is found in non-merging dialects (to make their dictionary more useful for other dialects), or apply one or the other consistently across the board. As a speaker with the merger, I tend to use ɔ in broad transcriptions, simply because it's easier to type on my IPA keyboard. Or, if I'm also representing the father~bother merger, I'll use ɑ, since it's the most peripheral of these vowels.

As to the exact pronunciation, it'll vary a lot, even within "General American"—a surprising amount of variation can fit under that label! Since there's no longer a distinction there, a certain speaker of a certain word might use something closer to [ɔ], or something closer to [ɒ], without it making a difference.