What is the ruling of eating bloody steak?
According to Syafi’iyyah scholars, there are two opinions presented. Imam al-Nawawi and Imam al-Subki ruled it as pure. While the opinion of some of the other Syafi’iyyah scholars stated that it is a forgiven najis and it is halal (permissible) to be eaten. However, if it is mixed with other foreign matter such as water used to wash it, then the blood on the meat itself is no longer pure and is ruled as unforgiven najis. This is final in the madhhab. If the served meat cannot be ascertained whether it is mixed with other matter for it cannot be observed, then its pure ruling remained. 
Allah SWT states:
قُلْ لَا أَجِدُ فِي مَا أُوحِيَ إِلَيَّ مُحَرَّمًا عَلَى طَاعِمٍ يَطْعَمُهُ إِلَّا أَنْ يَكُونَ مَيْتَةً أَوْ دَمًا مَسْفُوحًا أَوْ لَحْمَ خِنْزِيرٍ فَإِنَّهُ رِجْسٌ أَوْ فِسْقًا أُهِلَّ لِغَيْرِ اللَّهِ بِهِ فَمَنِ اضْطُرَّ غَيْرَ بَاغٍ وَلَا عَادٍ فَإِنَّ رَبَّكَ غَفُورٌ رَحِيمٌ
Say, “I do not find within that which was revealed to me [anything] forbidden to one who would eat it unless it is a dead animal or blood spilt out or the flesh of swine – for indeed, it is impure – or it is [that slaughtered in] disobedience, dedicated to other than Allah. But whoever is forced [by necessity], neither desiring [it] nor transgressing [its limit], then indeed, your Lord is Forgiving and Merciful.” 
According to Imam al-Baghawi, (دَمًا مَسْفُوحًا) is flowing or gushing blood. He presented the opinion of Ibn ‘Abbas who defined flowing blood as the blood which flows while the animal is still alive, has its soul and flows out the vein during slaughtering. This does not include the liver and spleen, for both are blood clots (not flowing blood) and both organs are halal (permissible to be eaten). It is also not prohibited to eat meat mixed with blood that isn’t flowing blood.
Imam al-Baghawi also included the statement of ‘Imran bin Hudair who said, “I asked Abu Miljaz regarding the meat which is mixed with blood or in a pot where there is some reddish colour of blood.” He then answered, “It’s fine, the blood that is prohibited is only flowing blood.” Ibrahim also said, “The blood in the brain and vein is also fine except for flowing blood that is put in intentionally.” Ikrimah said, “If it isn’t for this verse, surely the Muslims will try to find blood in the veins (trying to clean in great detail) following the practice of the Jews.” 
The law of the dietary rule for the Jews is called kashrut which obligates for every meat to be eaten to be clean and free from any blood. If not, the meat isn’t considered kosher (halal/permissible to be eaten). Meat with some blood in it will undergo the process of salting and broiling to ensure all the blood is removed from the meat. Alhamdulillah, Islam’s sanctions are not as complicated as this.
To conclude, according to the opinion of Imam al-Nawawi and Imam al-Subki, in my opinion, steak meat which is cooked rare, medium-rare, medium and medium-well as well as chicken meat where there are traces of blood in the vein and on the bones is halal and pure. I would also like to recommend referring to health or medical experts on the limit of its consumption for it might affect one’s health.