Jews are generally not considered to be PoCs. I know that- you don't have to remind me. Yet the racial/ethnic status of Jews is so convoluted and complex that I think it's worth bringing into the conversation.
To clarify: the most common definition of Jews would probably be that of an "ethno-religious group." What does that mean? It means that Judaism is a religion, but also an ethnicity/race. If you are ethnically Jewish but an atheist, you are still a Jew. If you converted to Judaism but have no Jewish heritage, you are still a Jew. However, for a large part of the Jewish population, Jewish religion and Jewish ethnicity overlap.
Now, onto the big question: Are Jews White?
There is really no easy answer to this question, and the history behind it is extremely complicated.
There are three generally accepted ethnic categories of Jews.
Ashkenazi Jews: European, White Jews. Think Fiddler on the Roof and basically every Jew represented in American mainstream media.
Sephardi Jews: Spanish and North African Jews. Physically, these Jews usually have dark skin and blend in completely with the people around them in Africa.
Mizrahi Jews: Middle Eastern Jews. Again, appearance-wise these Jews are indistinguishable from other Arabs and people from the Middle East.
Even for Ashkenazi Jews, however, the line is very blurred: despite looking just as White as many other Europeans, the antisemitism they face is usually based on race. It really goes to show how race is just a stupid, bigoted social construct. Here I'll address Ashkenazi culture, since the majority of Jews are Ashkenazi and that's the culture I grew up with.
So, not all Jews are religious. Actually, a lot of them aren't, especially in America. Whether you want to make a Jewish character religious are not is really going to determine how you write them, because the differences are huge.
Jews who aren't orthodox/hasidic usually don't wear anything that outwardly identifies them as Jews. They aren't necessarily Kosher, though many are. They'll go to temple/synagogue on holidays, but may not celebrate Shabbat every week. They will not get tattoos.
The most important holidays in Judaism are Rosh Hashanah and Yom Kippur- this is the Jewish new year, and is celebrated around September/ October every year, depending on when the day falls on the Hebrew calendar. There are many more holidays with many more traditions that can be easily found with a little bit of research.
You can't talk about Ashkenazi culture or customs without mentioning Yiddish. It's central to our identity. Yiddish is a mix between Hebrew, German, and Slavic languages traditionally spoken by European Jews. You probably know a bunch of Yiddish words that have been adopted into english: spiel, klutz, schmooze, and many more.
There are many different Yiddish sayings and idioms that many Jews will know of. If you want to make your Jewish character seem very authentic, definitely try to throw in some Yiddish phrases.
Jews have a very identifiable naming tradition which is why it's often easy to recognize 'Jewish names'. Not all Jews will have very obvious sounding Jewish names, however it is very common. Some common roots and suffixes for last names: Gold-, Schwartz-, -stein, -bloom, -farb, Feld-, -berg. Common first names: Rachel, Rebecca, Sarah, Max, Jacob, David. It's pretty simple to look this stuff up.
There are many different aspects of Jewish culture, and they are often strongly tied to religion.
Music is extremely important to Jewish culture. In synagogue, most prayers are sung/chanted and religious music is very important. Secular Jewish music is known as klezmer- again Fiddler on the Roof is a pretty good resource for this stuff. At celebrations, whether Bar/Bat Mitzvahs or weddings, we dance the hora, which is a traditional circle dance.
Food is also a huge part of Jewish culture. Some staples are bagels and lox, kugel, matzoh ball soup, latkes, challah and more. There are a lot of foods that are associated with specific holidays, while other foods are eaten all year round.
As in most cultures, family is also an extremely important aspect of Judaism. Traditionally, Jews only name their children after relatives who have passed away to keep their memory alive. The important holidays are usually big family gatherings, when both close and extended family come together to reunite and eat.
Please, please, please avoid the greedy, money-grubbing Jew stereotype. I feel like the reasons for this should be obvious, but it's still all too common. Jews do not control the banks. Jews do not control the media. Jews do not control the world. We are very, very tired of becoming the scapegoat for everyone else's problems. Please be sensitive to this issue and avoid any tendency toward antisemitic stereotypes.
Feel free to PM me with any thoughts/questions!