Jack of all trades is okay, but it's best if you pick one thing that you like best and specialize in it. Your other skills will help you in your day-to-day, but the deep specialization will help you with career advancement. Also don't forget to change the "one thing" if it becomes too untrendy... PHP developers aren't making what they once did, although PHP is still used all over the place.
"Jack of all trades, master of a few" is a better ambition. If you are in your 20s, your first goal is to become master of at least a couple of trades. Roughly 1-1.5 per decade.
As an employer I look for a balance. I look for the ability to have deep knowledge in at least one area, but also working knowledge in more areas.
Think of it as an S-curve that is steep in the 20s and flattens somewhere in the 50s. Those first 10 years after graduation are a bit special. This is where you either become really good at something, or you become mediocre (or worse).
(If you are a programmer and I see you spending 2 years on each programming language before moving on to whatever was trendy at the time: slim chance I will hire you. You will probably give lots of entertaining talks to conferences, but you will not accomplish much in real terms. I've seen people piss away decades of their lives like this, only to end up at the bottom of the food chain)
This sounds like good advice. I'm also employed at an early-stage startup and enjoy peeking into different areas in order to become proficient enough to be a founder myself at some point.
In contrast, I rather disliked my first student job in a more established company after a year for being too specialised.
Someone mentioned that a pi-shaped knowledge would be a good thing to aim for - I guess especially if they integrate well. I truly enjoy doing both Full-Stack Web Development (leaning towards backend) and Data Science (Python).