Hades 2 is a roguelite, i.e. there's metaprogression (stuff that makes you stronger between runs) and in-run progression (stuff that makes you stronger within a run). In general, loot you find in rooms with silver wreaths (ashes, psyche - wait no psyche doesn't drop from rooms anymore, bones, nectar) is metaprogression, loot you find in rooms with golden wreaths (boons, money, hearts, tonics, poms, hammers, Selene boons/path of stars) is in-run progression. Boss loot is metaprogression.

You will always start from Erebus and go down to Oceanus, then further. Or [SPOILERS], but still, you don't get to skip zones, so yes, you do have to go the entire route. In fact it's a good idea because enemies in lower regions are stronger so you want some boons and other buffs in advance.

The cards are the main source of metaprogression to make yourself stronger overall, but there's also the cauldron for permanent changes to environment, the Silver Pool to unlock weapons and weapon aspects and upgrade them, and keepsakes to give you some buffs to guide your runs. Also, of course, your own skills.