If you’re looking for practical ramifications of the resemblance between humans and apes, then consider R. Yose’s opinion in Kilayim 8:5:
וְאַדְנֵי הַשָּׂדֶה, חַיָּה. רַבִּי יוֹסֵי אוֹמֵר, מְטַמְּאוֹת בָּאֹהֶל כָּאָדָם.
The adnei hasadeh is a wild animal. R. Yose says, it[s carcass] imparts impurity in a tent, like a human.
What is this adnei hasadeh creature?
Tiferet Yisrael ad loc.:
בר נש דטור. נ"ל דר"ל וואלדמענש הנקרא אוראנגאוטאנג והוא מין קוף גדול בקומת וצורת אדם ממש. רק שזרעותיו ארוכים ומגיעין עד ברכיו ... מיהו ת"ק ס"ל דאע"ג דדומה לאדם בפרצופו ואבריו. אפ"ה כשמת דינו רק כשאר נבילות. ואמ"ט באהל.
This refers to the “mountain man”. It appears to me that it means the “wildman” which is called orangutan. This is a type of large ape, of the actual size and appearance of a human, except that it has long arms which reach to its knees ... However, the Tanna Kamma holds that although it is similar to a human in its face and limbs, nevertheless, when it dies it is subject to the same rules as other animal carcasses, and does not impart impurity in a tent.
So, according to Tiferet Yisrael, R. Yose holds that carcasses of orangutans (and maybe other great apes as well?) have some of the same laws of impurity as human corpses (and which do not apply to other animals) owing to their physiological similarities. The other sages, in contrast, believe that orangutans' similar appearance to humans is not sufficient cause for their carcasses to impart impurity in the same way as humans corpses do.