'Seemingly' is when something/someone appears to be something that isn't true. She was seemingly unaffected by the murder of her parents. The chicken has seemingly made him ill. The other use is when you are providing information based on the facts that you know. Pasta is seemingly made from some kind of grain. The car's engine has seemingly overheating. He seemingly enjoys being dressed as a woman. 'Apparently' is when you are talking about information that you have learned from another source but you are unsure if it is true. (After checking the weather forecast) Apparently, it will rain today. (You are unsure if this is true because it hasn't occurred yet). Apparently, Joanna told Sophie that I stole her wallet. (You do not know if Joanna actually told Sophie that you stole her wallet). John is apparently going to buy a new car. Brittany can eat 37 pizzas by herself, apparently. More good apparently examples here: https://dictionary.cambridge.org/dictionary/english/apparently

In AmE, “apparently” is much more common than “seemingly”. It is used regardless of the amount of evidence. It is also frequently used sarcastically. “Seemingly” expresses some doubt.

This isn't a direct answer to your question, but you might also be interested in knowing that the word "seemingly" is used far less frequently by native English speakers.

Apparent = obvious although it is commonly mistakenly used to mean the same as seemingly. Seemingly = not obviously true given the impression of being true. "apparently he has gone on holiday" = he told you he was going and now he is not at home, your are certain in your mind it is true and believe you are correct in your believe. "seemingly he has gone on holiday" = he is not at home and it is holiday season you are making assumptions. May be true may not be true, you cannot know for sure.

When you use the word, APPARENT, it shows more confidence and assurance. You would use this word when there was more evidence that things were true. For example, you might say, the motion of the earth around the sun is apparent because there is a lot of evidence. You would use the word SEEMINGLY when there was less evidence. For example, you might say, his intentions were seemingly honest because there is some proof. For things you are even less sure of you might you the word, PROBABLY. For example, you could say, the probable cause of a fire was arson because the evidence is unclear. Hope this helps.