This has been discussed over on ELL.
I think that the fixed expression have yet to (do something), meaning, as Collins says,
[to] have not yet (done something) we have yet to win
is potentially confusable with have to (do something), meaning 'need to do something'.
I have yet to treat a man with lupus.
which, though very formal, can mean that surgery isn't over for the day, even though 'I've never had to treat someone with lupus' is the more likely meaning. 'Yet', unlike 'still', can only be placed after and not before 'have'. Context will usually disambiguate between the modal 'still need to' and the non-modal 'as of now haven't' senses. 'I have yet to contact him' almost certainly implies that the speaker intends to try and that they haven't tried so far, as 'I haven't been able to reach him' would almost certainly be the choice for the other sense.
The expression be to do something has many senses. Relevant here are the 'moral obligation' sense
be to do something PHRASE FORMAL
1) used for telling someone what to do
[ie in the passive voice,
indicating moral obligation]
You are to stay here until I send for you.
but also the 'general arrangements' // 'preferred/intended course of action' senses (which I'd say overlap):
2) used for saying what has been arranged
The ceremony is to take place in the palace grounds.
3) used for saying or asking what should be done
What are we to do?
You are to be congratulated on your wise decision.
The bottom line is that both variants have different senses, which often overlap. Some individual examples will render the 'moral obligation / requirement / need' senses less likely or even inadmissible.
With 'I am yet to contact him', I'd say that the intended sense would normally be the non-modal 'I haven't contacted him to date', very similar to the 'have' variant. Using this for 'They still require/insist that I get contact him' would be a highfalutin' usage.