Are induction stoves considered inductive loads?
An induction stove isn't just an inductor connected across mains. A typical stove rectifies the mains power into DC, and drives the coils at a high frequency (tens or hundreds of kHz) through a resonant circuit. Ideally, the 'inductance' just provides a means for power transfer, and the load appears resistive. It is much like a voltage transformer. The main question is how the input rectifier &amp; filter behaves.

https://www.electronicsforu.com/wp-contents/uploads/2017/04/Screen-Shot-2017-04-14-at-3.22.46-PM.png
In the image above, the heating coil (cooktop) is represented by the inductor shown connected to the two IGBTs. The cookware itself (not explicitly shown here) is magnetically coupled to the heating coil. The 'resonant tank' refers to the combination of two capacitors, heating coil, and cookware. The MCU detects the resonant frequency of this group of components and drives the IGBTs near that frequency.
To answer your questions:

A typical inductive stove would use active power factor correction within the rectifier to maintain a PF close to 1, which should be better than a typical washing machine.
The coils are isolated from mains by the resonant power supply. You won't see the same inrush / inductive kick when turning the stove on /off as you would with a motor / inductor. These coils have a lower inductance and operate at a much higher frequency than a washing machine motor. Regarding your example, any loose electrical connection could cause arcing, regardless of the nature of the load.

I can't give professional wiring advice, but from an electronic perspective, an inductive oven should behave similarly to a other electronic loads, like your computer or TV. Which usually don't need special consideration.