As far as I have been able to see (I tried it out for a few hours and jumped right back into Rise of the Tomb Raider so my experience is limited), you level up your settlement with EXP by building things - more complicated crafts give you more EXP and so on, but for the character you just get Seeds of Life from doing certain quests to increase HP.

Battle system is basic hack'n'slash fare, but the only reason to fight enemies is to get their drops. Which allows you to craft better weapons, armour and stuff so you can improve your settlement to progress with the game.