If you were listening to music at that volume, it would generally be considered unsafe, and you would potentially have hearing loss beyond 37 minutes [1]
16 bits is plenty.
[0] https://en.m.wikipedia.org/wiki/Audio_bit_depth [1] https://www.cdc.gov/niosh/topics/noise/default.html
dB expresses the ratio of one value to another. So without knowing what the other value is, it's rather meaningless. But it is unfortunately an often-made mistake: how many times haven't you heard or read just dB as such? Anyway, this means you cannot simply compare dB dynamic range with dB used to express sound pressure level of which 'A-Weighted' is just one standard which gets used. Those are completely different things. Simply said, you can play 96dB dynamic range music at sound pressure levels which you won't even hear. Or at sound pressure levels which damage your ears nearly instantly.
And 96 to 119 is huge improvement.
First: Bits per sample just describe how many discrete amplitude values (2^bits) are possible at each sample of a recording. The waveform is quantized to these values.
To understand quantization in the context of dynamic range, imagine how many bits per sample are needed to recreate a very quiet sound without loss, and then check how many bits you need to extend that to reach very loud sounds in the same recording file.
For example: How much precision would you need to accurately record the sound of a pin dropping (10db)? 4 bits? 8 bits? 10 bits? 12 bits?
Let’s be really absurd and say we can use 4 bits — just 16 discrete values — to represent a pin dropping sound (10db) cleanly and indistinguishable from the real thing. This is so obviously impossible, given how terribly quantized the waveform would be, but let’s be generous and assume it works.
Now, for the same audio file to reach all the way up to 110db (not uncommon for bass drum hits in an orchestra for example) is an extra 100db of dynamic range, which is 100,000x the amplitude, which is a little over 16 bits in addition to the original 4. So, rounding down, we’d need 20 bits to represent 10db sounds (with quantization down to only 16 discrete amplitudes) and 110db sounds in the same recording.
I think it’s extremely obvious that even 20 bits in this example is far from sufficient. In fact, even 24 bits would be insufficient if 8 bits per sample are not good enough to record a pin dropping at 10db!