How to calculate the sample size when the frequency is less than 0.25?

Question

Mathematics

Task: Estimate sample size before running A/B test -> N
Given:

• significance (alpha) -> alpha
• power (1 - beta) -> power
• frequency (base conversion) -> P
• minimum frequency delta (minimum difference in conversion) -> delta

How I calculate sample size:
N = (Z _alpha + Z _power ) ² * ( 2 * P * (1 - P) ) / delta ² ,
where Z-values ​​are computed from significance and power.
But I came across an article that says that this formula gives pretty accurate results for 0.25 < P < 0.75. In other cases, a correction is introduced:
phi = 2 * arcsin(P ^1/2 )
N = 2 * (Z _alpha + Z _power ) ² / (phi ₁ – phi ₂ ) ²
Link to source: medstatistic.ru/articles/sample_size. pdf
From here I have three questions:

1. Do you really need to make this adjustment for conversions below 25%?
2. If a correction needs to be introduced, is the correction formula for this problem correct:
   N = 2 * (Z _alpha + Z _power ) ² / (2 * (arcsin(P ^1/2 ) –arcsin ((P – delta) ^1/2 ) )) ²
3. And just in case: is the first formula by which I count the sample correct?