Okay you need to understand a few things about Ahri first.
She is not an ADC. Ashe and Jinx are hyper carry ADCs that are slow and immobile, and generally lack true Burst potential. However, once they meet a certain threshold, output ridiculous amounts of DPS. On the other end, Ahri sits in a weird spot in the middle of okay DPS synergistic with her kiting play style and okay Burst potential if you play your Assassination just right. In trade for her weird damage niche, she's outfitted with an insane amount of mobility for a Mage like herself. Her forte is not power, it's flexibility and offering you options. She's a jack of all trades: capable of doing so many things, but not necessarily the best at any particular thing. You'll never appreciate Ahri if you compare her in a 1 to 1 stat test in a very specific scenario against a certain champion, she almost will always underperform at another champion's strengths. However, once you realize she's capable of so much more than most champions, you ought to appreciate her better.
Also, pitting a Mage against the Dragon is literally the most unfair comparison you can make. The vast majority of Mages are literally unequipped for fighting any Dragon at all in the first place.
So to answer your question. She's actually a rather solid mid laner in general, and one of the champions above her in Mid Lane is Yasuo, making her the third best Mid Lane Mage in the overall category according to champion.gg. She's the opposite of weak, she's statistically very powerful. As for expectations of a Mid Lane Mage, she's capable of almost everything all Mages are typically capable of (Burst Potential, Ranged Poke, Wave Clear, etc.) but she doesn't do anything in particular too amazingly. She breaks the standard mold of a Mage slightly in that she's hyper mobile. Other than that though, she's a special case in terms of Mid Lane expectations. Finally, it's extremely totally unfair to compare her directly to Ashe and Jinx. Ashe and Jinx share enough traits that it's fair to compare them to each other, but Ahri is her own champion with her own unique skillsets and outputs. Direct comparisons literally do not work, and the majority of them make Ahri look straight up inferior which is just wrong.