Changing behavior once you’ve given notice always makes you look bad.

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Changing your behavior after giving notice of resignation can harm your reputation. Maintaining consistent behavior is crucial, as drastic changes, even if positive, can make colleagues perceive you as inauthentic. It's essential to continue doing your job and leave on a positive note to ensure you are remembered well in the industry.

Don't Act Differently After You Give Notice

It would be great if colleagues actually applied it. Most of them leave and then forget about their duties in the following days.

I feel like this is common sense? While you would be resigning, during the time that you are still in your current company/organization you still have responsibilities that you are expected to handle. In my personal opinion, if you still have work before you leave you’d be too busy to worry to actively shift your behaviour.
Alas, this is my personal opinion and how I would handle things.

I once heard a quote; “People remember the first and last impression of you more than anything else, and it forms their perception of you if you meet in future”

I generally agree with these suggestions. But I will say, in my opinion, there are scenarios where they should be broken.
If the leadership has a history of punishing employees for being critical about bad decisions, I’d say it’s a perfect opportunity to be an advocate for your teammates and voice your concerns during your final weeks. Be the advocate for change that others don’t have the opportunity to be. Being abnormally vocal isn’t necessarily a sign of an inconsistent employee, and can instead be a sign of a hostile work environment.
Additionally, it’s not appropriate for you to be taking on new tasks in your last couple weeks. You should be doing knowledge transfers, handoffs, anything to get all the stuff currently on your plate off of it to ensure a smooth transition. This is to ensure your team doesn’t have to scramble to fill the hole you leave once you are actually gone. So if management is dishing out new tasks to you even with a foot out the door, I say it’s better to push back, delegate, and focus on handoffs. You won’t be doing business as usual during your final weeks, and therefore this inconsistency should be expected.