Haaretz is often objective by global standards, but is a minority in Israeli media unfortunately. I prefer them to know what's really happening on the ground.
Al Jazeera and Middle East Eye are both Qatari funded, and both tend to be biased to the Islamic viewpoint. That being said, Al Jazeera does invite a lot of experts with opposing viewpoints to their channel regularly, in both their English and Arabic versions, which is how they eked out their name as the most trusted and most viewed media source in the Arab world.
Other news media like Arab News (Saudi), The National (UAE) and Al Arabiya (Saudi) are largely propaganda machines. You won't even get reliable news on what's happening inside their own countries, forget elsewhere.
Sometimes TRT World (Turkey) puts out spicy bits of news that is usually underreported elsewhere, but they're basically the RT of Turkey.
Russia Today, in normal times, often presents a very neutral perspective of Middle Eastern news, especially when most of Western news media is biased towards or silent on Israeli actions. In fact, for most of the attacks reported on GCC countries, RT was and is likely still the most accurate of them all. But of course, these aren't normal times, and their service practically acts like Tasnim English version when it comes to news on Iran.
Also good to remember the English versions of Israeli sites have the propaganda for the US and diaspora. The Hebrew versions give a clearer picture of the internal messaging.
Yes, this is very important when approaching the region. If you want to get the actual pulse, you have to read from the regional language website. For example, Al Jazeera Arabic is actually very extremist by Western standards, just as Israel Hayom in Hebrew is.