Straight up, I should mention that I am not a bird photographer and do not have much experience in this area. Hopefully someone with more experience can offer an answer with more specifics.

Preferred Zoom Range

However, the bird photographers that I know all seem to gravitate toward use of 150-600mm zoom lenses (that ... and techniques to allow them to get closer to shy birds without scaring them off.)

Even lenses that zoom up to 300mm seem to not be enough. Canon makes a 100-400 and even that doesn't seem to be enough. Use of a teleconverter is not desirable as it creates focus issues.

Auto-focus and Focal Ratios

The focus technology used in the cameras (when using the optical viewfinder) relies on passing the light through a beam splitter and detecting the phase-difference of the light. But this system only works well at low focal ratios (e.g. f/5.6 or lower ... even f/6.3 is fine for most cameras). At f/8, many cameras are no longer able to reliably focus ... but a few models can operate at f/8. I am not aware of any camera that can use phase-detect auto-focus above f/8. And this is the problem with teleconverters used with long lenses.

A 70-300mm zoom will typically have a variable focal ratio of f/4-5.6. At the 300mm end, it's lowest focal ratio is f/5.6 (f/4 is only available near the 70mm end of the zoom range). When you add a teleconverter, you multiply the focal ratio of the lens by the focal length multiplier (e.g. if it's a 2x teleconverter then you multiply by 2). This means 5.6 becomes 11.2 (f/11) and no camera can use phase-detect autofocus at f/11.

A Canon 100-400 f/4-5.6 lens coupled with a 1.4x teleconverter effectively becomes a 140-560mm lens and at 560mm it's lowest focal ratio is f/8 ... and some cameras can still use some of the auto-focus points at f/8 (but expect auto-focus speeds to be slower). So this solution can work but probably isn't ideal.

And I think this is the reason why most bird photographers tend to prefer the lenses that natively have the 150-600mm range (and these are usually f/4.5-6.3 but the camera can auto-focus at f/6.3).

Lenses

Your budget will factor into your choice but here are a few options:

Sigma 150-600mm F5-6.3 DG OS HSM | S -- this is Sigma's top-end 150-600mm zoom. The final letter "S" is "Sport". Unsurprisingly it is also their most expensive lens offered in this range.

Sigma 150-600mm F5-6.3 DG OS HSM | C -- this is Sigma's less-expensive offering. The final letter "C" Is "Contemporary". This lens sells for about half the price of the "Sport" version.

Tamron SP 150-600mm F5-6.3 Di VC USD G2 -- the "G2" version is Tamron's newest (generation 2) version of the lens and it is the more expensive model.

Tamron SP 150-600mm F5-6.3 Di VC USD -- the non-G2 version is the older design for Tamron but they still make and sell this lens. It is significantly less expensive than their newest version.

Sigma and Tamron make these lenses with mounts for a variety of manufacturers (e.g. Canon, Nikon, Sony, etc.) so if you do choose one of these, make sure you order the lens in the Canon-mount model.

Again, I am only offering that these are the lenses used by most of the bird photographers that I have met. I have no personal experience with any of these lenses ... but offer this list as a starting point in your search.