[1]: https://www.gog.com/game/day_of_the_tentacle_remastered
[1]: https://www.gog.com/game/day_of_the_tentacle_remastered
[1]: https://playclassic.games/games/point-n-click-adventure-dos-...
I ended up doing it anyway at the time, but later I would play all three, and the third one really benefits - in my view anyway - from having played the first two ones, even though they can all stand on their own. So I wonder whether Day of the Tentacle is similar?
They address this in the linked article (also from personal experience) -- you really don't need any context from Maniac Mansion to thoroughly enjoy DOTT and they are really totally different games in style and substance.
BTW: In the version of DotT I played in the 90s there was a funny easter egg: A computer in the game was running a playable version of Maniac Mansion. I don't know if this is part of the remastered version though.
Agree on not needing to play Maniac Mansion first, too. I came to the original having no idea that MM even existed. The characters and story are great even if you don't know the references.