Your requirements are conflicting:
Omnidirectional, yet high gain ("best range possible").
The best you can hope for is high efficiency, so that power isn't being lost into, say, the FR4 (which isn't the greatest dielectric at radio frequencies). If that's always true (or good enough), gain and directionality are inversely proportional.
There's no such thing as a true omnidirectional antenna (which relates to the "Hairy Ball Theorem" in mathematics, interestingly enough), so you'll have to settle for dipole, or dipole-like, which gives about 2dBi (i.e., 2dB above isotropic, assuming it were possible).
If you need more range than this provides, you must sacrifice directionality (and size!).
So if this is all within your expectations, great.
So on to the much more important question -- will it work?
If the antenna is tuned poorly, it may not work at all! You need it to resonate very close to the operating frequency. This looks to be a 1/4 wave type, so its bandwidth should be okay*, and it won't need to be cut terribly accurately to the frequency. You should be able to solve the rest by substituting parts in the antenna matching circuit (all the L, C and R parts on that side of the chip, I suppose).
*Which also implies it could be smaller -- you still get a dipole radiation pattern, but the physical size can be smaller. Small antennas couple more poorly to space, so they need to be tuned more precisely, and need to be even more efficient, to achieve the same gain. The smallest size antenna is one that just barely covers the ~2MHz bandwidth that BlueTooth requires, but this would be very precise to actually manufacture. Still, this explains how most IoT radios can be so small.
Oh, and you may want to add more stitching vias near those matching components.
Final FYI: if you're just making one-offs, it's probably "who cares". But if you want to sell this thing, you'll need CE certification for an intentional radiator. That's expensive, and it's a very good reason why radio modules are so common these days. The module itself (with integral antenna, or a connector suitable for a limited range of appropriate antennas that can be attached to it) is CE certified, so that the rest of your product doesn't need to be.
Tim