It always depends on what you want to shoot, what your budget is, how much do you want to carry, and what your base camera is.
Since I believe you use Panasonic bodies, the 100-300mm mark II lens is a nice lens and it is more affordable than say the 100-400mm lens, and the lens OIS should work well with the sensor shift IS in the recent Panasonic bodies. I have it, and it is a decent lens, though at times I prefer my classic 4/3rds 50-200mm + EC-14 + MMF-3 setup. I did have an issue with the 100-300mm mark II with an ocean splash during a whale watch, so I don't feel it is as splash resistant as my Olympus lenses (note the 100-300mm mark I did not claim to be splash resistant).
The Olympus 100-400mm, Panasonic 50-200mm, Panasonic 100-400mm, and Olympus 150-400mm lenses are more specialist lenses with corresponding higher prices, and bigger/heavier lenses. But if you are using them full time to capture birds or wildlife they are better than then 100-300mm. Obviously with a Panasonic body, you probably want the Panasonic 100-400mm or the 50-200mm lenses for dual OIS and sensor shift IS support.
The 14-140mm (or the Olympus 14-150mm) will give a bit more range, but not dramatically more. But it is an advantage that since it covers the 14-140mm range, in good light, you often don't need to change lenses. I used the Olympus 14-150mm in many years as my main vacation/outdoor lens. Two years ago, I updated to the Olympus 12-200mm, and it is nice to have both the additional 12-13mm range as well as the 151-200mm range. In the last 2 years in fact, the 12-200mm has become my default lens, with the Olympus 12-40mm f/2.8 lens now taking second place.
If you don't have other Olympus/OM lenses, the zoom and focus rings rotate in the opposite directions between Panasonic and Olympus/OM lenses. Last week, I was in Florida and doing a bit of birding. I had the Panasonic 100-300mm mark II mounted on the OM-1 and the Olympus 12-200mm mounted on the E-m5 mark III. I had to remind myself when switching cameras to change the direction I rotated the zoom ring.
Getting one of the fixed lens cameras with a long zoom range is another option, particularly for lighter usages. If you stick with the Panasonic models (FZ300, FZ2500, and I don't remember if the FZ1000 is still in production), the interface should be similar to what you are currently used to. And perhaps the battery is the same (my FZ300 uses the same DMW-BCL12 battery that my G85 uses, which is convenient). Due note, that the sensor is smaller and possibly the lens is slower, so these cameras aren't as good at high ISO as your micro 4/3rds gear. Of course if you don't normally carry 2 cameras, carrying the 2nd camera can be an issue (or possibly you choose to take either the fixed lens camera or your micro 4/3rds camera out for shooting depending on what you are going to shoot).