Is it bad if the laptop is plugged in all the time (only when it's on)?

I'm not sure if the battery is broken if you plug it in whenever you use it.

Is that harmful?

I suspect your laptop has a Li-Ion or Li-Po battery. As far as I know, these should ideally be kept between 30 and 80%. Accordingly, I deduce that a permanent 100% charge is not good.

If you mainly use the laptop on the mains, you can perhaps discharge the battery to ~ 80%, then shut down the laptop and remove the battery.

No guarantee.

Should I plug it in while gaming?

The power supply goes out when the laptop is full. If you then use one percent of the battery, the power supply comes on again and charges to one hundred percent. This is not good for the battery then it wants to be charged all the time.

Can you somehow adjust it so that it goes further down?

It depends on the laptop.

Many laptops have a battery management system, which can ensure that exactly what the answer from Ceeesy759 says happens automatically. In this case, a permanent connection to the mains should not cause any damage.

When the laptop is connected to the external power supply, the battery is charged. Li-ion batteries do not like it at all when they are charged to a high voltage for a long time. It is therefore better to remove the battery from the device if it is only used with an external power source. If you want to store the battery for longer, you should charge or discharge it to about half of its capacity.

How do I know if the battery is already damaged?

Laptops from the last 5 years can also be used in network operation. That means that the battery does next to nothing and everything is operated directly via the external power supply.

Just let it run without mains power until the battery is empty. If the time corresponds approximately to the new condition or the technical information, everything is ok. If it's, say, 20% or so less, it's still good.

In this case, a permanent connection to the mains should not cause any damage

Well, yes! Even if the battery management interrupts the charging process at 100% and thus the battery is not permanently charged, it is then permanently in a state of charge of> 80%.

My Sony Vaio laptop has a great function. I can choose to charge the battery to a maximum of 50% or 80%. Then he switches to mains operation. It has had the original battery for at least 12 years (that's how long it is in operation - by then the battery has probably already been 1 year under its belt due to storage etc.)

Well, with a 12 year old Li battery you should assume that it no longer has full capacity, only a fraction of it. These batteries age, regardless of whether they are full, half empty or (almost) completely empty, just at different rates.

Around 60% charge status should be the best choice for storage, so it's true, 80% or more are not as lifespan-friendly, you just have to know what you want: Always one possible. Long-term operational laptop without mains power or optimized battery life.

Well, with a 12 year old Li battery you should assume that it no longer has full capacity, only a fraction of it. These batteries age, regardless of whether they are full, half empty or (almost) completely empty, just at different rates.

Agree with you, I didn't say anything to the contrary ;-),

Around 60% charge status should be the best choice for storage, so it's true, 80% or more are not as lifespan-friendly, you just have to know what you want: Always one possible. Long-term operational laptop without mains power or optimized battery life.

Agree with you, I even mentioned it myself with my other comment ("[LiPo or Li-Ion batteries] should, as far as I know, ideally be kept between 30 and 80%.")