ADDITION is derived from Old French, so it is used later in English, 14cLate adoption. additional, the 1640s only started to be used, additionally definitely later.
I didn't find out when I started using in addition, but I was able to find out when I started using in addition to 1680s. In current usage, in addition is equivalent to in addition to something (when something is obvious in context, or when the speaker doesn't want to highlight something). However, whether the etymology is in addition earlier or in addition to earlier remains to be further explored.
At present, in addition is used much more frequently than additionally. The chart below is from Collins**.
The author speculates that there may be two reasons why additionally is not popular (and some even think that additionally is informal):
First, because it is no less than in addition characters, and the pronunciation is more laborious than in addition (purely personal inference).
2. In addition can be connected to something, but additionally cannot be connected to something.
It is also because of the second point that in addition with to something cannot be replaced with additionaly, such as.
Example sentence 1] she's a fitness instructor in addition to being a full-time student.(In addition to being a full-time student, she is also a fitness instructor.) [Cambridge Dictionary of Senior Scholars].
Example sentence 2] in addition to these arrangements, extra ambulances will be on duty until midnight(In addition to these arrangements, additional ambulances will be on duty until midnight.) [Oxford Dictionary of Senior Scholars].
Example sentence 3] there's a postage and packing fee in addition to the repair charge.(In addition to the repair fee, there is also the cost of postage and packaging.) Collins Dictionary of Senior Scholars].
If there is no to something, in addition and additionally are interchangeable, such as.
Example sentence 4】additionally, we request a deposit of $200 in advance(In addition, we require an early deposit of $200.) [Cambridge Dictionary of Senior Scholars].
Example sentence 5】there is, in addition, one further point to make(In addition, there is one more point to be clarified.) [Oxford Dictionary of Senior Scholars].
Example sentence 6】in addition, students can take classes in other languages(In addition, students can take courses in other languages.) Collins Dictionary of Senior Scholars].
Note: When in addition and additionally are at the beginning of a sentence, they are followed by a comma;However, there is no need to add a comma before and after additionally in the sentence, because the -ly ending of the adverb that marks it does not cause difficulty in breaking the sentence, but there is usually a comma before and after the addition in the sentence, so as to facilitate the breaking of the sentence (a bit like an insertion).
additionally, if it is only "to a degree further" (not "one more"), then it should not be replaced by in addition, such as.
Example sentence 7】The birds are additionally protected in the reserves at birsay(The birds are further protected in Birsay's Sanctuary.) Collins Dictionary of Senior Scholars].
Example sentence 8] he will sign a personal guarantee to additionally secure the loan(He will sign a personal guarantee to further secure the loan.) Collins Dictionary of Senior Scholars].
Before Middle English, in meant upon, at.