Why is it other countries' job or responsibility to take care of people living on Israeli territory?

If Israel didn't want to accept the people on the land it acquired, it shouldn't have acquired the land.

Why hold and occupy land if not willing to accept the people living on it as citizens and grant them equal rights?

The land is in Israeli hands now. This is Israel's domain. It's on them to grant these people rights and citizenship.

If not, then Israel should abandon all claims to the land along with the people they don't want to accept as citizens living on it.

It's silly to blame Jordan and Egypt for not taking in refugees from land they haven't controlled in decades and which Israel now does. Given that Israel is such a modern, developed, prosperous, wealthy, democratic, innovative country - founded on Herzl's ideals of coexistence - then surely it has the resources to integrate refugees into society - unless they simply don't want to due to some racist or discriminatory prejudice.

Turkey has taken in more refugees than any other country - nearly 4 million (twice the population of Gaza). It's population is only a million or so larger than that of Israel.

Germany has taken in 3 million refugees, though granted its population is much larger. However, its GDP per capita and wealth is similar to that of Israel.

Israel - with a similarly developed economy and wealth - can't take in any if they're not Jewish? Even those that live within Israeli territory?

I think it's Israel refusing these people citizenship and rights, not UNRWA. UNRWA isn't a government or country. They can't grant citizenship. Israel can.

Besides, Israel banned UNRWA so whatever status it designated or granted is irrelevant now anyways.