After 3 months since approval/in 3 months since approval

The main difficulty with your suggestions comes from your use of since.

Since = from a particular time in the past until a later time, or until now

Cambridge

Whereas

After = following in time, place, or order

Cambridge

{A} It is therefore inappropriate to use since to refer to a time in the future. Use after. “The info will be seen 3 months after approval.”

{B} If you say “will be seen in 3 months” it will be understood as “will be seen at the end of the 3 months that start now”.

{C} If you say “will be seen 3 months after approval” it means “at the end of the 3 months that start when approval is given”.

{D} If you say “will be seen in 3 months, after approval”, the comma is needed to introduce a phrase that qualifies “3 months”. The meaning is that it will be seen 3 months from now, and that approval is expected within that 3 months. There is also a hint that, if approval is not given, it will not be seen. If you omit the comma, “in” is not needed, and the sentence reverts to {A} above.