I don't think Finnabair was killed by the Templars, for days she had been acting different, the MC noticed that she seemed thoughtful about something, and wasn't acting like usual, and she confirmed it.
Then there was the training, where King Oberon showed up to train him in Finnabair's place.
He knew where Finnabair was, but didn't want to say, and I don't think they started the war with the Templars while the MC was with them, and even if that was the case, they would have used someone other than Finnabair, the MC's guide, the one he was living with.
She was most likely part of the group that wanted war, and her changing her mind may have caused unrest in the group, and Finnabair, the one who had been accompanying the son of the leader of the Templars, having been killed by a Templar, would rekindle the desire for war, whether true or not, rumors are usually enough.