As a related add-on question (that is connected): I heard that one theory is that the Philistines were part of what's known as the "sea people". How likely is that? It'd certainly explain why they're not mentioned in the Bible (because they are, but not called Sea People).

There's a lot of debate about who the "Sea People" were and what exactly the Late Bronze Age collapse actually was. Given such uncertainty it's hard to make any definitive statements about them.

Weren't the Israelites in Canaan, chilling out, or whatever?

According to the traditional narrative, the sea people would have been doing all their stuff during the Egyptian captivity or slightly before. More than one scholar has suggested that a foreign dynasty from the sea people was the "Pharaoh who knew Joseph not." That is to say that it may have been the sea people that enslaved the Israelites. Another theory is that the Israelites were part of the sea people. They may have been part of the foreign dynasty and they were enslaved as part of the reestablishment of native dynasties.

Probably the most popular theory at the moment is that the Israelites never had a period of Egyptian captivity or Exodus. Instead they are likely to have been Canaanites who slowly developed a separate national identity and mythology. As such everything prior to Samuel, Kings, and Chronicles have to be taken as mythological just so stories. Why was Judah in control of Idumea? Because Esau (the Edomite ancestor) sold his birthright to Jacob (the Judaean anscestor). If anything we'd be surprised to find any actual history in the Pentateuch and Judges.

The Torah/Pentateuch likely didn't take its current form until around the 6th or 5th century BCE. So it's not too surprising it doesn't detail what happened 600-700 years earlier; particularly when we don't really know what happened. The various authors and redactor were far more interested in providing an origin story than they were in providing an accurate history. Even if the authors knew about the sea peoples hundreds of years before, they only would have been included if it were relevant to the tale they were telling. And that was the history of Israel and their relationship with YHWH. At the point where the sea peoples were active either the story has the Israelites in Egypt having forgotten YHWH or in the desert renewing their ties with YHWH. So as far as the primary biblical purpose is concerned, the sea people are an uninteresting side show.