Drag USB stick with boot info to another data carrier?

Yes, the question is correct. I have Ubuntu on my USB stick, which has to stay in the laptop permanently. But it only has 15GB of it free about 3. Can I drag everything that is on it onto my 63GB stick and remove the 15GB stick so that the 63GB stick becomes my permanent one?

And how do I have to format it virher?

Grab clonezilla boot that and simply clone from one stick to the other then adjust the patitions size and you're done

Yes, that is possible.
Almost every backup program can "clone" - this is the name of the function.
And since regular backups should also be made with Linux, you should, strictly speaking, already have such a program. 😉

Otherwise I like to refer to https://www.linux-magazin.de/ausgaben/2016/03/bitparade/.

What does partitioning actually bring

Why should I "already have such a program"

Because otherwise you are one of those danger seekers who do not make backups.
("No backup? No pity!", As it is in admin circles. 😉)