“Telephoto” has varying meanings from a technical (focal length is longer than actual length) to a “it’s long”, so can be rather meaningless in advertising copy.

Low-light handling is as much to do with the body of the camera as the lens - the lens just gathers light, its the body and its sensor that offers the sensitivity (and you may find mirrorless cameras better at that).

A low-ish aperture number, such as F4, will certainly help in low light but will also add to price and weight by quite a bit (F4 on a 800mm can lead to a silly price!). So, keep it as low as your budget allows for the focal length you want.

The focal length will depend on whether full-body sensor or a crop sensor - if the latter, then 400mm might well be ideal, but for the former, for wildlife such as birds, I’d suggest more like 600mm if you can. If its the local badgers, that’s different.

You might also want to consider zoom - adds to the cost, but adds to options.

Background: I had a lot of pleasure with a Canon R6 + F11 RF600mm (which is something of a budget lens) taking wildlife shots, and often in poorer light (up to ISO2000 or so gets OK shots, and can go much higher for “ID” shots) - I’ve upgraded to a much better (heavier, more expensive…) lens, but that’s outside your budget. The Canon R6 was always billed as good in low light - ironically for having fewer pixels (there’s a trade off).

Given you don’t want RF lens, I’d strongly recommend looking at 2nd hand Canon (or Sigma!) lenses from a reputable source - ideally a competent local camera shop offering a years guarantee on the lens or the like. Don’t just buy from Ebay!!! Many camera enthusiasts have moved to mirrorless (for good reasons, though DSLR still has one or two reasons to use), and Canon therefore cater far more for that market - which means smaller range of new lens, and lots of 2nd hand lens on the market as using EF-RF adapters sucks.

Nice shot, but what sort of fox is that, it certainly doesn’t look like a Red Fox from the UK.