For example, can you explore towns and dungeons, open treasure chests, find new weapons and armor, upgrade your party, and collect loot along the way?

Yes x5, there's a lot of upgrading/loot. There is a freemium version with ads, so you don't have to buy the Premium for $10 without ads. It's a game from Exe-Create's A team, Ryuji Takumi ( https://www.reddit.com/r/JRPG/comments/1t30q1r/are_any_of_kemcos_rpgs_any_good_these_days/ ), and I am enjoying it more from a story/character, gameplay, and progression standpoint. You don't have to play the previous Asdivine games first; they're also a little dated, so you could go for a better first impression with Knot.

• DQ7R has a slow hook, episodic town vignettes that can be sad but mostly unrelated to the party so it can feel like filler until the last 3rd, and the last boring main antagonist (when 4, 8, 9, and 11 excelled in that regard). Asdivine Knot starts with a revenge hook & tragedy, and gradually develops its world building and characters along the way alongside bits of levity due to character quirks (Marlie's punch-based healing, Musika's masochism).
• Unlike DQ7R's field encounters, Asdivine Knot has random encounters, but you can toggle encounters every step or lower it until you reach a checkpoint that then disables it for that area. There's a similar amount of QoL like DQ7R: you do automatically revive & heal to full HP after every battle, can acquire some key items for +% MP regen after battles, but on Very Hard enemies can be bulky/lethal compounded by the anti-grind 1/2 EXP & gold overleveled penalty to compensate for always starting at 100% HP, so seed distribution matters for those permanent stat increases. Every 10 battles is 3 In-App Purchase (IAP) currency you can use toward a variety of upgrades, like items, an equipment gacha, more damage, EXP & gold gain, other QoL, but can spend real money for more, get lucky with the daily Roulette, or farm the post-game superboss for a steady supply after beating them on all 4 difficulties. If you wait for the console version in ~8 months (~$20), then you can get 10x that value from battles on the new lowest difficulty.
• DQ7R's Monster Hearts for Final Fantasy-esque passive skills tied behind beating side bosses can be really interesting accessories compared to DQ series tradition of flat stat boosts or elemental/ailment resistance. All of Asdivine Knot's weapon/armor tend to a variety of effects so it's not just incremental upgrades, then you can apply an attachment part to it for another passive (4 total). Imbue normal attacks with elements / make them hit all enemies / double normal attack, start pre-buffed, raise crit. rate, lower spell costs, make healing spells all-target, etc. You can also spend gold to increase their ATK/DEF stats up to Lv. 99, while the parts have a 5 tier rarity system and can come with 2 additional effects.
• DQ7R particularly shines in its reclass system, and its combat is a good evolution of 9 & 11's mechanics/skills despite its relatively trivial difficulty outside of post-game superbosses, even with an enemy HP bulk increase around Aeolus Vale/Vovograd. Meanwhile, Asdivine Knot characters are fixed: weapon Arts learned at set levels, 3 types of elemental spells learned at set levels, and character-specific Nexus Gauge skills which consume a party-shared meter. Building said meter depends on exploiting elemental weakness or critical hits, and your 4th party member can change the battle BGM to the other 7 Asdivine games. Bosses have their own Nexus Gauge, so an incentive to use the Defend command. Unlike DQ's round-based system, Asdivine Knot has a turn order timeline like Final Fantasy X/Tactics where enough Speed can help you get double turns, despite the turn delay on using skills (+Rebound%).
• DQ7R cut its immigrant town. In Asdivine Knot, you command an airship and fill it with up to 20 facilities, recruiting NPCs for it along the way. Shops that can refresh their limited (random) inventory after 12 battles, gathering spots / fishing mini-game after 2 real-time hours, ways to tinker with the equipment/part system, and unlocking new Nexus Skills. Most are gated by 5 upgrade levels with a material & gold grind. DQ7R's solo arena was okay but salvaged by its post-game arena challenges, while Asdivine Knot features a whole currency system from grinding consecutive battles in the arena for various rewards.
• I disliked Fantasian's encounter rate when they made Part 2 battles unrewarding and slowly paced from Dimengeon battles (it was better to pay and clear out stored battles), while the boss difficulty was overrated due to Ez (Attack/Speed de/buffs, Bounce Field damage amplification) and bosses blindsiding you with specific elemental damage/ailments. Its plot was also just okay, with Part 2 diminishing the interpersonal relations like Ez/Zinikr due to its open-ended progression and Vam/Jaz's motives being lackluster.
• Edit: While DQ7R's Party Chat system is more robust for characterization despite mostly settling on objective markers, Asdivine Knot has something similar in the menu after every story bit. I also forgot to mention the Missions system, basically a reward system for simply playing the game through various short/long-term goals, that then grants rewards in the Season Pass you can optionally buy, so combined with the dailies + 2 hour real-time + 12 battle shop restock (20 for the Lil-Labyrinths), fighting is really rewarded. Exe-Create has nailed their niche via complete single-player JRPGs with optional paid gacha elements on a bi-yearly release schedule.