How does a laptop maintain battery at full?
That basically depends on the manufacturer.

I've had one laptop that would indeed fully charge the battery, then switch to battery power until it dropped to 95%, then restart charging. The battery died within six months, and I haven't bought from that vendor since.

Typically, the battery is disconnected when fully charged, and then monitored for self-discharge, and after dropping to a certain level, it is again fully charged. This level is chosen as a trade-off between limiting the amount of charging cycles and risking a less than full charge. Again, different vendors choose different values here, between 98% and 85%.

As an extension, some controllers also differentiate between continuous power with the battery level dropping below a threshold, and being plugged in while the battery is below the threshold (many devices are unplugged for short times while moving to another room), look at current power usage (if the computer is turned off, the supply may be unplugged soon), number of batteries installed, past charging behavior, ...