Sorry, this is not going to be cheap or lightweight.

Some zooms up to 300mm are reasonably priced, but anything longer than that, zooms or prime, is going to be very expensive.

If you don't need image stabilization or zoom, 400mm f/5.6 could be one option, but it doesn't bring far away subjects much closer than 300mm. From 300mm to 400mm the jump is not that big (but on the other hand, your 75-300 has very low image quality which doesn't allow much cropping unlike with Canon's 400mm that's perfectly croppable). Also, Canon's 400mm f/5.6 costs nearly 1000 EUR used. However, the 400mm f/5.6 has very high image quality, so with your T7 that has 24 megapixels, you can simply crop your images if 400mm isn't enough. In daylight, your shutter speeds can be set to be so fast that most 400mm image aren't shaken. However, near sunrise or sunset a 400mm f/5.6 without image stabilization won't work.

Another option is 150-600mm zoom from Sigma or Tamron, at about 1000 EUR new, slightly cheaper if used. However, third-party lenses with the Canon system often have slight autofocus issues. Also I doubt it that 600mm zoom from these third-party manufacturers would be much better than cropping a 24 megapixel image taken with Canon 400mm f/5.6. Furthermore, these 150-600 zooms weigh a whole 2 kilograms!