No, you should not leave you laptop plugged in like this it will be overcharge.
Over the years this question has been posited many times.
Here are two web links about this:
2. https://www.youtube.com/watch?v=jAcgld6gtyo finds a test with the common battery we see in laptops kept at a full SOC (state of charge) for 3 years. The result is so little was lost but let's keep going.
My view is from the office where we leave laptops plugged in for years. It's not uncommon to cycle out a laptop that has been plugged and find the battery has no to little wear.
-> The first link covers a KEY FINDING. Ready?
A. "You Can’t Overcharge the Laptop’s Battery".
This was an issue decades ago but those laptops are dead and gone. If you have one from 20 years ago, treat it as you should for that era technology.
-> The second video along with other sites are finding that the SOC (state of charge) has little effect on life when we leave it at full SOC.
B. Leaving laptops plugged in for years does not degrade the battery.
Between jehugarcia's video, my own experience with 5 year on power laptops and other IT staffers in many companies, I'm calling this one DEBUNKED.
-> From the Howtogeek, other sources, where is the battery wear occuring?
C. Using the battery does wear it out. (sorry for the obvious finding here.)
And this is how we arrive at the new phone, laptop and other things that use Lithium battery rule today which is ABC (always be charging.)
I've seen over the years folk expend a lot of effort try to save their laptop battery life. Turns out it wasn't as tough as it seems.
Final thought: YES, do use your laptop's battery life extender option if it has it. It does work for all the reasons you'll find above. But removing the battery? You're working too hard with little to gain.