We are yet to discover....

Does anyone else cringe?

No. The OED is clear:

Yet (adverb - senses relating to time)

With following infinitive referring to something which has so far not happened but might be expected to happen in the future (e.g. yet to be done implies ‘not done so far’, ‘not yet done’ and police have (or are) yet to arrest any suspects implies ‘police have not yet arrested any suspects’).

Frequently preceded by has or have (later also is or are) .

Another No from me.

If anything is or has yet to be done, the statement infers that someone or other has decided the step is necessary but so far (= yet) has not done anything about it.

I agree OP that you cannot say "Is it been done yet"; you could, however , say Is it done yet`? So, no, I am quite happy with this usage.

No, I’m happy as it is

My poor old grammar Professor is turned in his grave, poor lamb.

'We have yet to do it' or 'This has yet to be done' sound a bit forced to me. The OP's grammar professor must be sleeping very uneasily if he would turn in his grave at 'is'.

But I would probably say 'This is still to be done'. How does that rank?

TBH I cringe at ‘Are we done it yet?’ and ‘Is it been done yet?’
but never at, ‘We are yet to discover…’ or any such usage.