Having gotten a bit farther in Eternal City I've unlocked some additional features.
The 'Dark Bazaar' to my surprise is an auction house that lets you buy/sell items to other players, a rare feature in gachas I feel.
'Spacial Tempest' is the games form of 3 player Co-Op. Matchmaking is fast, or you can do it with friends, but it's easily completed on full auto, which even continuously queues you for the next match, and exhausting all of the day's possible (diminishing) rewards takes a while of letting it run for better or worse. Gives 1 Opal (premium currency), 100k+ gold and a bunch of equipment fodder per day.
And 'Competency Trials' is a daily challenge mode. You pick one of the three daily recommended characters (or free pick for worse rewards), and you're given a set of 7 different challenges to complete 4 of to advance (such as defeating a clone, running to the end of a maze on a timer, fighting a boss solo, etc). After which you're given a chain of 10 traditional fights to win. Daily clear awards 5 Soul Shards (the currency that allows you to rank-up characters, awarded when pulling dupes via the gacha. I believe this means gacha pulls are completely unnecessary!), a few other currencies, and first-time clear with specific characters increases their maximum equipment cap.
My biggest issue with the game was the slow stamina regen but these modes add a lot of extra gameplay time. And while it didn't launch with one, I've read that there will be stamina-less events to play later.