This one is completely different from your typical ARPG, but I'm going to recommend Noita.

It's a 2d game where you play as a wizard off spelunking. The magic system is rad as heck, you find wands with spell slots in them, and spells that you can put in the wands. You can rearrange and combine spells to get some truly bizarre effects

I've killed myself in a dozen hilarious ways trying to make the perfect wand. It never gets old

Elder Scrolls 3: Morrowind lets you fly around, jump over whole cities, and kill most NPCs with one high powered spell. It's a very unique game, but if it clicks with you there's nothing quite like it. Vibrant modding scene too.

The base game is certainly playable, but if you want modern resolutions and some vanilla-friendly bug fixes OpenMW is an open source recreation of the engine, there's instructions on their website.

Badass wizard eh? Try Magicka! 😁

Skyrim has some mods that go really deep on magic and combat strats.

Kingdoms of Amalur has very fun, very flashy combat. The rest of the game is really ehhh, but if you just want to blast magic and have cool skills then it's a great choice.

ARPG: Path of Exile, Last Epoch, Grim Dawn.

Also consider the survivors/bullet hell kinds of games: Vampire Survivors, Soulstone Survivors, etc.

It is mayor jank but Dragons Dogma was the closest to feeling like a mage I've ever experienced. There are no cool downs in the game but channeling spells takes some time and upholding a continuous spell drains your stamina. In this setting the art of a mage was reading the battle and estimating how much space you have to channel spells, several of which can easily break the encounter wide open.

Edited since neither my English nor my autocorrect were working as intended.

noita is insane and has absolutely zero handholding. it's truly hardcore and kinda souls-like in difficulty/lore, but truly excellent!

magicraft is the king in casual spell crafting, very good game to play a bit after work, can call it quits anytime and pick it back up again. just had it's full launch as well and might still be -20% (about 12€)

fictorum is fairly unique, because it's first-/third-person and 3D, and also very good with an intuitive spell system and a little bit of indie game jank

Dark Souls. If you play a mage, you'll be on easy mode, which very much does feel badass in a game so full of terror.

If you are cool with CRPGs may I suggest Arcanum? Probably has one of the most weirdly in depth magics systems.

If you never played Magicka you should give it a shot.

Have you played Dragon Age Inquisition? I hadn’t until someone here recommended it, so I grabbed it for $3 and am deep into it. As a mage, it’s full-throated magical glory. You can use lightning, fire, and ice magic, get badass staffs, and have a good combination of AoE and normal spells. I definitely feel OP after crafting some custom armor and weapons. Lots of fun.

I’ll give a shout out to Fictorum, which is kinda janky but is a physics-heavy wizard simulator with on-the-fly spellshaping and some real wild spellslinging combos. Between the combat levels, there’s a travel/encounter-type rpg thing vaguely similar to FTL as you try to stay ahead of a wave of Bad Things^tm^

Fictorum is the game that most scratches the wizard itch for me. It's an indie game, so don't expect AAA polish, but what is there is absolutely what you might call a "hidden gem".

Hogwarts Legacy. Combat is fast and brutal.

The side stuff feels kind of bland mechanically and something about the open world doesn't capture me like I want it to, but it's pretty good pure magic combat.

Its kinda different but maybe Two Worlds, I remember killing everything in the world and resurrecting literally everything so that every NPC was friendly to me. I killed the whole world and brought it back.

Terraria has some really fun mage gameplay.

Yeah lots of recommendations here but let me give you some that I think answer your request more specifically.

Wizard Of Legend is a top down roguelite where you play a wizard that can equip different spells and upgrades. The combat and strategy is very focused on spells and how good you are at slinging them between dodging enemy attacks.

https://store.steampowered.com/app/445980/?snr=1_5_9__412

Margoq's Lair is a top down roguelike where spells are cast by composing them from elements, for example fire + shield casts the spell fireshield. It makes for a much more satisfying experience than pressing a button to cast a spell.

https://store.steampowered.com/app/2516550/Margoqs_Lair/

I'll go a different route. Control.

Wayfinder. Recently discovered it and i've been having quite a bit of fun with it. It's a former live service converted to singleplayer/coop, so the story kind of blows. But it's a good ARPG - a Torchlight meets Warframe sort of thing.

Two Worlds II

Story is generic and it's a little bit jank, but has one of the best magic systems in any game I've played.

Btw, have you played something like Hades? You're not technically a wizard, but close enough. And there's other hades-like games which might be more "wizard-like".

You should try Oblivion

For just a solid combat system, hogwarts. Was really surprised. They had some solid people design and build it. Really stood out against the rest of the game which wasn't bad by any stretch just repetitive. There are some serious combat challenges too. Just make sure you play on hard. It really needed one difficulty higher tbh.