So what is the classification of this oscillator circuit? It is not a Hartley nor a colpitts.

​

 

It looks a bit like an attempt at a COLPITS oscillator It might possibly be a VACKAR type, maybe. And given the feedback arrangement it may not oscillate at all.

 

It definitely works, I have built several in my life. Think common base, non inverting positive feedback is provided by C2. In most cases I have used it as an RF oscillator and transmitter it can go to quite high frequencies.

 

<blush> I used the wrong type transistor in the drawing I'll repost the schematic,.

 

Found a link (sort of):
https://www.next.gr/oscillators/rf/

​