I think your analogy regarding search warrants is a bit flawed because Senate confirmations are bound by different rules and expectations.
It’s generally far from illegal to be (overtly) racist or write racist things on the internet but the Senate generally sees that as disqualifying. Jeff Sessions failed to get a federal judge position during the Reagan administration over allegations of racism, including testimony from his former deputy who was a black man.
Senators didn’t pass his nomination due to those allegations, which are obviously not illegal.
Sexual assault and rape cases are particularly tricky because a very significant number of them go unreported entirely or surface many years later.
In some cases beyond the statute of limitations. The catholic church is a great example.
Dr. Ford’s case is passed the statute of limitations if I recall correctly but I have to verify.
Applying the same legal standard as a criminal trial to any Senate confirmation would do more harm than good in my view. If there is a statute of limitation, that person would be untouchable even if he did it. If it’s a he said/she said case, that person would also be untouchable even if he did it.
That’s why credibility is most important in my view, not so much fulfilling the burden of proof standard of a criminal court trial.
I think the point of an FBI investigation would be not to draw conclusions but to get other witnesses under penalty of perjury and corroborate or refute testimony. Then the Senate can make a more informed decision on credibility.
Under penalty of felony for lying to Congress is near useless when the number of convictions for lying to Congress is almost non-existant.
Even the arguably most significant case, a Reagan administration official associated with Iran/Contra, had his convictions overturned.
In the case of Mark Judge for example, the questioning was conducted by Grassley’s chief counsel Mike Davis, who previously tweeted (and deleted) "Unfazed and determined. We will confirm Judge Kavanaugh. #ConfirmKavanaugh," before hearing Dr. Ford's testimony. That’s not a good look.
If Mark Judge would say the same under penalty of perjury to an impartial FBI interview it would provide significantly more credibility.