You can leave the power adapter connected almost all the time. It will not overcharge. It will not do it any damage.
For best long-term battery life, you should plan on using it on battery alone at least once a month.
There is no longer any need to deeply discharge the battery. Doing so will not improve battery behavior in any way.
But this is a tool for you. Use it the way it is most convenient for you. If you need to run on the battery for a long time, that is what you should do.
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