Can I take one month break between two jobs?
Absolutely. This is perfectly normal, especially in the US where longer vacations are otherwise rare. For most people, especially high-performers with busy schedules, the downtime when changing jobs is one of the few real extended breaks they can enjoy.
Would it leave a bad impression with my future employer
Only if they have communicated a very urgent time line to you and wanted you to start as soon as possible. In those cases it can come across as tone deaf that you're taking a full month off. But even in those cases it would be fine so long as you're upfront with them and properly discuss your time line. A four week break can be hard to sell in some parts of the world but if you stick to your guns a reasonable employer will accept that. Great employers will understand the importance of disconnecting and will welcome the fact that you can start mentally and physically rested. If it comes up, offer some version of "The earliest I can leave my current employer is the Xth and I plan to take a full month off to recharge and take care of some things I've been putting off."
If you're worried they might try to negotiate you can open that conversation by stating that you'll take five or six weeks off but are willing to reduce it to four or some equivalent there-of.
Needless to say you should have this discussion on time line with this prospective employer before you resign from your current job and ideally before you accept their offer. If they originally were fine with a two month notice period and are suddenly pushing back on getting you started earlier when they find out you're "only taking a vacation" that's a potential red flag as it indicates a cavalier attitude towards disconnecting and taking time off. That might impact your decision to accept their offer.
You already have an agreed-upon start date but if you hadn't this question covers that discussion.