A “feature” that comes with the battery’s portability is limited capacity. A power intensive circuit, especially one with moving parts could use up the available energy and discharge the battery very quickly. Plan for this in your project with things like switches to cut off and save power while doing other activities.
@Arjan - Windows default power settings are generally to conserve more power at the expense of performance when running on battery. However, if AC power is connected then the battery is not needed, after all, the PSU can supply enough power to charge the battery AND run the laptop. @Bruce - no more so than any other PC.
Batteries also provide very stable and clean power, although you have to consider the discharge curve. Batteries follow chemically and physically determined voltage curves as they discharge. Fresh batteries usually have a high initial voltage (sometimes even just a surface charge) that rapidly declines.
To wrap up, it is possible to use a battery charger as a power supply but with some disadvantages. If you want to use one as another, you should first check the voltage and regulation to make sure they are compatible. Also, you may need to change the polarity depending on the device you are using it with.
However, if AC power is connected then the battery is not needed, after all, the PSU can supply enough power to charge the battery AND run the laptop. @Bruce - no more so than any other PC. They use a switchmode PSU which are normally fairly resilient to crappy power.
Batteries are great for powering projects on breadboards, PCBs, and just about any circuit. They’re very portable and come in a lot of form factors; with different voltage, current, and power capabilities. If your circuit is in need of portable power or temporary power, batteries can be exactly what you need.