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Will the Escape from Tarkov be a session-based shooter? What game modes is it going to have?

In the classic meaning of this term - no, the game won’t be session-based. It has several playing modes. The player only has one life, and, with dying, he loses everything that was brought to the location or found in it.
The first and essential mode will be available with the game release, the story mode. The game session (typically an hour or hour and a half long) will take place on a large, about 5-10 sq. km., open location. The player will have to consecutively clear all of these raid scenarios, with several possible exits, each determined by the game story. By completing one scenario, the player unlocks the next one. Players can return to the previously unlocked scenarios in search for particular loot or more detailed exploration (which can lead to the uncovering of side quests and locations)..
When all scenarios (there will be around 10 of them) are completed, a free roam mode will be unlocked. In this mode, player can move around a 15 sq. km. area without any time limits. Moreover, the game is going to have an Arena mode, which closely resembles gladiator fights.
Thus, although EFT technically does have a session in the scenario mode, it is only determined by the story, where player’s character has to escape from Tarkov. The free roam mode will have no time limitations, and in the Arena the game session will be limited by death either of player’s character or his adversary.