The entropy of the TOTP distribution is −log2(2148/2147483648)×483648×2148/2147483648−log2(2147/2147483648)×516352×2147/2147483648 ≈ 19.9315685303 bits.
So yes, the difference in entropy is negligible. The TOTP distribution is worse by 39 nanobits (3.906e-8) per code.
Pedantry 2: normally in cryptography we use the min-entropy <https://en.wikipedia.org/wiki/Min-entropy> rather than the Shannon entropy that you linked, though in this case they are almost equal.
Exercise: consider a weighted, million sided die. 50% of the time when you roll it, it comes up 1. The other 50% of the time, it comes up on one of the other 999999 results, with equal likelihood. What is the min-entropy of this distribution? What is the Shannon-entropy? This should tell you why the min-entropy is preferable.
Added: hmm I think I made a calculation error further up. I'll look at it tomorrow if I can.
Not being an expert, I was unaware of this and worked through it after reading the article you linked.
So you have 1 bit for the min-entropy and about 11 bits for the Shannon entropy. The Shannon-entropy pretty much hides the elephant in the room, which is the enormous bias of rolling a 1. So basically in crypto you use the min-entropy because that reflects the most vulnerable scenario in a system which is what you prioritize protecting against, rather than protecting against the average scenario.
The entropy of the TOTP distribution is −log2(2148/2147483648)×483648×2148/2147483648−log2(2147/2147483648)×516352×2147/2147483648 ≈ 19.9315685303 bits.
So yes, the difference in entropy is negligible. The TOTP distribution is worse by 39 nanobits (3.906e-8) per code.