It all depends on your intended output. And how important "sharpness" really is to the individual image.
How big are you planning on printing? Are you going to be cropping the image? Does your image rely on "tack" sharpness for the message you intend to convey with it?
There are many famous photographs that are compelling on every level that aren't really *tack* sharp. For example, many of Henri Cartier-Bresson's most famous images are a bit blurry, this for example:
Yet it is an amazing image that speaks volumes.
If you want to see how sharp your particular lens/camera combo is, then you need to shoot in a controlled environment. Indoors where wind isn't an issue. On a decent tripod. Tripping the shutter with a remote release.
Sharpness is somewhat dependent on gear. It is somewhat (moreso?) dependent on technique. It's importance is dependent on subject and intended output. You are the only one that will be able to determine if your current lens/camera is delivering what you want it to deliver.
Remember that format also plays a large role in this. Crop format vs full frame. Medium format vs 35mm "full frame" format. Large format vs medium format. Certain lens/camera combos can push you to the extremes of what a given sensor size/film size can produce, but each format has very real limitations. No 35mm equivalent camera/lens combo, regardless of price, is going to approach the detail possible with a large format film camera. The physics just doesn't make it possible. But you have to decide which compromises you are willing to accept in price/convenience/immediacy/capability/versatility/image quality.
While it is possible that an "L" lens will produce sharper images than your current lens, it is also possible that improving your technique by using a tripod, using a remote release, paying more attention to your exposure choices (ISO/aperture/shutter speed) could result in sharper images. Totally possible that your technique is good and that a gear upgrade makes sense, but I'd think about the other things if this is really a big decision for you. Would also make sense to consider how important *tack* sharp images are for your creative vision and intended output.