These arent easy questions to answer.
Currently we might argue against the accuracy of Luke, however we have a number of examples of othe biblical historical claims where they seem to be inaccurate that were later proven and others where the jury is still out
Pontius Pilot 1 - for centuries it was claimed he never existed!
Kind David - again, it was claimed he never existed
The Hittites - claimed they never existed outside of the bible
The israelites in Egypt and the Exodus - its still claimed that this has absolutely zero historical support because we can find no direct evidence for it (despite it being the cultural history of a current race of people with a worldwide population about 15.7 million people…pretty difficult to say isnt true)
Paul being bitten by a poisonus snake on Malta - there is no evidence that we have yet found of any poisonus snakes having ever existed on that island