Not actually.
The transformer has multiple taps besides the one for the filaments.
2.2VAC with 125mA is about 250mW. I really don't want to add a transformer the size of a small apple for 250mW

I guess there's also a 5VAC tap as well but I prefer to derive the needed voltage from 5VDC as I'll be using to power everything.
There was a single IC doing all the work for the VFD and oven UI. It's a 54 pin chip that I could find no info on. It's written S-674GP AEICC9578623 on it.
That's why I'd prefer to generate a square wave of about 3.1Vp with 50% duty cycle to power the VFD filaments. I guess I'll install it back into the oven for temperature measurement and timer or stuff like that.
The 555 timer works good, it outputs a 100KHz square wave of 50% duty-cycle with an amplitude of 4.6V. But I can't power directly as the 555 can't do more than 100mA and it's not good practice. Also the output must float above ground as I know, need to do some more research.