table 7.3 perfectly reproduced, the previous errors are confirmed as numerical problems

The discrepancy is due to the numerical problem.
The raw data has four digits after the decimal point:
for example
t y

1990 1 17.5534000000
1991 2 21.8601000000

but on fpp webpage only two digits are kept:
t y

1990 1 17.55
1991 2 21.86

In non-exponential smoothing, these errors can be cancelled because the expectation of the sum of these errors is zero.

In contrast, in exponential smoothing, the expectation is not strictly zero. The error can be accumulated.

Actually we do not need to get into too much of this issue.

At least, table 7.3 has been perfectly reproduced, it shows that the HoltWintersNew() function works well on exponential smoothing.