Background Information: Germany, Junior Dev, female, mid 20s

I am leaving my current job in the middle of July because of: Sexual Harassment, helpless and scared

I have a new job lined up for me starting August 1st, that is also the date written in the contract. After signing the contract my new employer told me I could start earlier and to just give him a call.

Reason for this was, that when I interviewed for the new job I was not exactly sure when my end date will be, and I am still not sure.

Because of the "struggles" at my current work I really feel the need to take some time off. I do not want to take time off in the first few month of my next job in fear it might make a bad impression.

So I was planning to go spend a week between jobs relaxing and trying to get the old job out of my mind. But this raises a couple of questions:

Can my next employer find out? Should I tell him beforehand?

Am I obligated to start earlier if I can, even though it was only an informal request from my next employer?