Will my wife be divorced if I swear by divorce that I will not search for a scientific page on the Internet, and then I search through screenshots of the same page with the intention of divorcing my wife? And is it permissible for me to take her back without her knowledge and without witnesses if the divorce occurs, especially since she is still a virgin?

Entering the search query into the screenshot, regarding the oath you swore, depends on your intention when you swore the oath or the reason for the oath. If you searched the screenshot believing you would not violate your oath, then it is most likely that you did not violate it, and your divorce did not occur.

If the divorce of your wife occurred before consummation, the majority of scholars hold that her divorce is ba'in (irrevocable), and you do not have the right to revoke it except with a new marriage contract. As for the Hanbalis, they consider valid seclusion (al-khalwa al-sahiha) to be equivalent to consummation in establishing the right of revocation, and this is what is issued as fatwa by us.