I'm wondering exactly in which situations forces between bodies are, and are not consider to be tidal forces in the context of planetary and astronomical science.
Don't overthink it. All a tidal force is, is the net force you get when two gravitational forces aren't quite the same. The force of gravity is the first derivative of potential (the "slope"), whilst the tidal force is the second derivative of potential (the change in "slope"). The classic example is spaghettification. You're falling into a black hole, and the force of gravity is greater at your feet than at your head. So you get stretched by a tidal force.
If two rigid, non-deformable spherical masses with spherically symmetric mass distributions orbit each other, can we say there are no tidal forces or tidal effects there?
No. Like Mark said, the tidal force is independent of your non-deformable spherical masses.
If one of them has a permanent, static deformation (e.g. quadrupole moments and higher) are there tidal forces then? If both do?
There are tidal forces because one side of each object is closer to the other object than the other side is.
Or are dynamic, induced deformations required before we invoke the "T-word"?
No deformations are required!
Can tidal forces be radial, such that they do not tend to raise or lower an orbit over time, or must they have tangential components, like the one that is slowly raising the Moon's orbit?
They're usually radial. The simplest case is where one object is falling straight towards another much larger object. Things get more complicated when you've got two large orbiting objects like the Earth and the Moon.
Is it possible to draw a clear line here, at least within the scope of this SE site and This month's focus tag which is tidal-forces?
Probably not, because to really understand the tidal force you have to understand the force of gravity. A lot of people don't, even though Einstein made it clear. I said something about that yesterday in this answer, but I don't think it was appreciated.