I was assuming that we are discussing DSLRs - the E-mount mirrorless cameras are not considered in that category by most people I know. I think they fit into the four-thirds forum on this site.
I'm sorry for the confusion - I was assuming you are talking about Sony A-mount cameras.
Andrea
The E-mount cameras are not in the M4:3 forum or category, in that they use APS-C sensors rather than M4:3 sensors...however, you're correct too that they would not be considered DSLRs and since the O.P. (of this topic) mentioned that they bought an SLT Sony model, that would be an A-mount camera.
In E-mount, there is currently only a maximum telephoto lens in native mount of up to 210mm, with a 240mm zoom coming next year. With teleextenders, the reach can be extended by 1.7x, for a maximum equivalent of 535mm on E-mount.
In A-mount, there are plenty of long-lens options, some of which you already mentioned: Tamron 150-600, upcoming Sigma 150-600, Sony 70-400, Sony 500mm F4, as well as older Sigma 50-500, 150-500, 170-500, Tamron 200-500, Minolta 300mm F2.8, 300mm F4, 400mm F4.5, and 600mm F4...plus a few more I'm not naming - and any combination of 1.4 and 2x teleconverters, both matched and third-party.
I shoot with both an E-mount camera and an A-mount camera for birding, so I'm quite familiar with both. For my Alpha DSLR, I currently have the Minolta 300mm F4 plus a 1.4x TC, and the Tamron 150-600mm. For my A6000 e-mount camera, I have the 55-210mm lens plus 1.7x teleextender.