Thank you! This is great news.
Fujinon XF 55-200mm f3.5-4.8 R LM OIS has got nice price, and its aperture in the range of 55-80mm is a little faster than on Fujinon XF 16-80mm f4 R OIS WR that I own, but at 200mm it's f4.8 which I can't tell is usable. I bought 16-80 for indoor sports but also for general purposes like landscape and architecture to complement my 35mm f1.4. For indoor sports, I used it in the range of 50-80mm so far, and I needed some more zoom, but I also know that at some other gyms that I've been before even the 35mm was fine when I could place myself near the court. Not sure if 55-200 is ideal solution for sports either, but it's much cheaper and lighter than 50-140. Heck I think even f2.8 is too small aperture for indoor sports. If I don't go for 50-140, I would most likely go for 55-200.
The push function on the rear-dials of the 'earlier' X cameras is quite prone to defects. I believe it was solved in the X-H1 and the X-T3 thereafter, but X-E3's have the earlier internal design. The push function could 'stick' in one function or between functions causing the rotate function not to work properly. If that happens, internal cleaning or replacing is the only option. Something that (most of) you can't do yourself.
Hi Milos, welcome. I'm too a Leica M user (M7 and M10-R) but I also use the X-Pro2. First, about the firmware updates. You can update straight to v5. Every firmware update contains the full firmware and not just the changed bits.
As for the lens, Fuji has two zoom lenses that might work, but they are both a bit slower in terms of aperture. It's the 55-200 and the 70-300. Both have IOS (the X-Pro2 has not) so that is a benefit. Yet, I believe the 50-140 is the better choice for indoor sports even though the X-Pro2 isn't exactly fast in AF.
Another option might be the long prime lenses. There are two in this category (I won't mention the 200mm): the 80mm macro is very sharp (allows for cropping) and has OIS but is is almost as expensive as the 50-140 and is not easily available as second-hand. The 90mm tele is one of Fuji's best lenses for portraits, is less expensive than the 80mm, but lacks OIS. It focuses very fast though. I loved that lens, but you need to learn to work with it esp. on an X-Pro2. The 50mm f2 is a very nice lens by the way and if the focal length works for you, you can crop by up to 30% (approx. 14-16MP) before quality becomes an issue.
The OVF of the X-Pro line doesn't work well with lenses longer than 50mm and the EVF of the X-Pro1 and 2 is a TFT-type that doesn't work well in low light and fast action (indoor sports). It has a poor refresh rate and in 'smears' a bit when you move the camera fast. You can however, learn to work with it even though it's not ideal.
As for third-party lenses, I'm not aware of a fast 'long zoom' for X-mount. Tamron announced some lenses for X-mount (so did Sigma) but not in this category as far as I know. Their variable zoom lenses very quickly go to f4.5 or f5.6 once you zoom in. Viltrox and others focus on shorter primes for X-mount.
Fuji claims that it is exactly the same EVF (Sony-made OLED), but to my recollection the refresh rate of the X-T3 is a bit higher. The main difference (re. the EVF) is the processor of both cameras. The X-T3 has a later generation processor that allows for higher refresh rates. Make sure both cameras are in 'boost' mode when you compare them. Also other features (like brightness and color setting) can cause difference in EVF experience as well as minor changes in the optics in front of the EVF. Fuji isn't specific about changes re. this.
I can't compare anymore since I sold both cameras and switched. From that experience I can tell that the same EVFs on paper can make a great difference in practice. So, always check the EVF yourself before you buy a camera. Esp. when you wear glasses or need to change the diopter.