Adult clothing no. But for kids clothing you kind of need it, because without the cutting function attaching rubber bands to neck, wrist, and belly seams is very difficult.

TLDR : "nice to have, but not a necessity"

For some basic jerseys (think T-shirts) a basic zigzag is fine to begin with. That 100EUR sewing machine will have some fancier stretch stitch options that are slow, but "good enough" to look like an overlock (but can't do the cut of course).

If you have the space / money, overlock is definitely what I'd get as a second / third machine. It's much quicker / cleaner if you're working on jerseys or shirts.

But I still keep wearing the T-shirts I did when I was starting. On my list the first thing to do is to understand how to alter something to fit you. It can be done by hand (needle and thread), but to be reasonably efficient, the BOM would be "sewing machine, box of pins, scissors, piece of chalk / ruler and something to press / iron".