The Sony A7 II uses the E mount lenses. You can get E mount in 2 different sizes...APS-C or Full Frame. Basically the size of the hole in the back of the lense. You have a full frame sensor so with a full frame lense you get the full 24mp of your camera. Your camera can also use APS-C lenses but it will only use a portion of the sensor equivalent to APS-C size and the resulting picture will be about 10-12MP or so depending on if you shoot in 3:2 or 16:9 mode. The A7 II has a crop mode setting for using APS-C lenses. The Sony has a crop factor of 1.5x so that 55-210mm lense would be equivalent to 83-315mm.
If you can, go for a full frame lense and take advantage of your $1800 camera.
The bad news is there isn't much support for E-Mount yet. E-Mount was designed for Sony mirrorless cameras that are light, compact, and have DSLR quality. Take a DSLR Canon lense for example and Sigma can do a minor tweak and make it Nikon or Pentax compatible. An E-MOunt lense requires a whole new design. That's why there is not much from Tamron, Sigma, and Rokinon/Samyang in the E-Mounts.
That being said Sony has a 70-200mm F4 full frame Emount that is around $1600. An F 2.8 version is over $3000. Those are pro level lenses that match up quite well with the pro level of your $1800 camera. With an $1800 camera it's expected that you will invest many times that amount in lenses. Lenses can last a user 30+ years while some people upgrade camera bodies every 2-3 years. It's not uncommon for pros to have a $1000 camera with over $10,000 in lenses. Using a $400 lense with an almost $2000 full frame camera seems kind of pointless but it's possible.
So I checked all the Sigma, Tamron, Rokinon stuff and there isn't much. Sony has that 55-210mm in APS-C format as you said. It's small, light, portable, and the picture quality is not terrible. Not great but not terrible. It's a great value. But if you can swing it that 70-200mm F4 is a great lense. Being F4 it'll allow about 3 times more light than the F6.3 of the cheaper lense which would be better. You can compensate by upping the ISO which results in grainier pictures, or reduce the shutter speed with induces blur or requires a tripod. F 2.8 is when you enter the realm of night photography such as city streets at night or indoors like at a club, concert, wedding reception where it's dark. You can also see how expensive it is.
The F2.8 is 1480g, The F4 is 840g. The F4-6.3 is 345g. You can see the big difference here. The F2.8 is over 4 times heavier. the F2.8 is also almost twice as long. So you can see the advantage of the cheaper lense as a walkaround lense. The full frame lenses are also weather resistant to match your camera body.
Hope this helps you out without you getting too discouraged with E-Mount stuff
Great cameras but not quite as common as Nikon/Canon stuff. The only reason Nikon and Canon sell soo many cameras is they had tons of lense options and people who own thousands of dollars worth won't get rid of it all to change camera brands. Build the lenses and people will buy your cameras.