How to release a stuck gas stove knob

I would say that this is highly dangerous. It is against US and Canadian code to not have outside ventilation for any fuel-burning appliance in your home; that's your furnace, HWH and stove/oven, assuming all are NG or propane. It is only acceptable to have a "filter-only" vent hood for your stove if it's all-electric (which BTW is the case for every single apartment I've ever rented; gas appliances may be cheaper on utility bills in the US, but a gas stove is a huge fire hazard and general liability for any landlord).

The code is in place for a very good reason; not only can inefficient burning of fossil fuels produce carbon monoxide and smoke (both of which continue to cause damage long after you've reached fresh air), but even when these fuels burn ideally, they remove oxygen from the air and replace it with CO2. CO2 in itself is not toxic in the same way CO and soot smoke are; as soon as you reach fresh air the symptoms of CO2 asphyxia begin to dissipate, while soot and CO poisoning ("smoke inhalation") can kill you hours after you reach fresh air. However, the consumption of oxygen and production of CO2 in a space with inadequate ventilation is a double-whammy for anyone in the same space; the oxygen is being consumed so there's less of it even in upper strata of the room's air, and as the CO2 builds it settles downward in a "blanket", pushing oxygen up towards the ceiling and away from you.

As the CO2 level builds, your body's natural "inhale/exhale" reflexes go haywire in a Catch-22 condition called hypercapnia; your natural breathing while in a high-CO2 atmosphere actually increases the CO2 levels in your blood, but the only thing your body can do to reduce CO2 levels is breathe. So, you start hyperventilating, which only exacerbates the problem. Should you pass out from lack of oxygen, you will not wake up if someone else doesn't get you out of the room or get some ventilation of fresh air through it.

Your landlord is running illegal housing. However, he may not know it, so be nice at first. Follow standard procedure for maintenance requests, and ask the landlord to install a proper outside vent line for this fume hood. If he refuses or drags his feet, you can call in the city's Code Compliance officials, or federal HUD (Housing and Urban Development) representative, and they will MAKE the landlord comply. Depending on the terms of your contract, the landlord may be giving you a free out by not living up to his end, meaning you may be able to break the lease at no cost if this has gone on for some time with the landlord's knowledge and inaction.

Understand that the cheapest way for your landlord to fix the problem with tenants still occupying the units may well be to cap off the gas feed and replace all the gas cooktops with the cheapest electric setups he can find. If this was the reason you moved in, and you don't get a "free out" from this debacle, you may find yourself stuck with a spiral-coil POS.

I started this as a comment, but it started getting long, so here goes.

Without more detail and pictures, I would recommend calling in a local expert to look things over, just on the basis of not having you taking a half-baked, uninformed guess from an anonymous person on the Internet as a reliable answer.

Having said that and meaning it...

Is there a control lockout feature on your stove? That would prevent it from supplying gas to the burners (leaking gas into your residence) after a power loss.

Is there a gas valve on the stove itself that got turned?

Otherwise, you probably just have the gas shutoff valve for the stove turned off. Typically (unless it's old), a gas valve will have a yellow handle or knob, or possibly a red or plain brass one. But it will tend to be a valve that rotates just 90 degrees rather than a round knob that you turn multiple times to open or close the valve. Although, it could be a rotary valve.

If it is a newer 90 degree valve and installed correctly, it will be open if the handle is aligned with the pipe, and closed if the handle is perpendicular to the pipe. Although, another caveat, there are also valves built on elbow fittings. I've attached a couple of example images below.

Offhand, it sounds like there just isn't any gas getting to the burners on your stove. Any link to the bidet is probably incidental, since you already know that you were turning both water and gas supply knobs around the house trying to make the water stop. I doubt that your bidet has its own gas supply, and the "flexy tube" is probably just water, right?

You should have a separate gas valve for each gas-fired appliance, somewhere close to the appliance. You have to be able to turn the gas off for just the stove so that it can be disconnected and removed (maintenance, replacement, etc.) without turning the gas off for all the other appliances in the residence. The gas shutoff valve for the stove should be somewhere near the stove so that if you disconnect it, you aren't evacuating all of the gas in the line between the stove and the main gas valve into the residence.

You could easily have the main gas supply valve open, have the gas valve for the water heater open, but have the gas valve for the stove closed.