What is "silanol activity"?
Silanol activity is perhaps an informal term which is quite frequently used in the chromatographic literature to explain the poor band shape of primary amines. Other amines show this too but to a lesser extent. That is why you will not find a formal textbook definition of silanol activity. One might also see the term silanophilic interactions used occasionally. If you look at the surface of silica gel, you will see that a silanol group, is like an alcohol analogue, except that silanol is slightly a stronger acid.
If we disperse silica particles in water, and let it stay there for sometime, the pH of water is &lt; 7 (around 3–4, if I remember correctly). So the point to keep in mind is that silica is acidic due to its ionizable silanols.
There are different types of silanols as drawn in this paper: Sunseri, J.; Cooper, W. T.; Dorsey, J. G. Reducing residual silanol interactions in reversed-phase liquid chromatography: thermal treatment of silica before derivatization. J. Chromatogr. A 2003, 1011 (1-2), 23–29. DOI: 10.1016/S0021-9673(03)01070-7.

Now if you are doing chromatography of relatively strong organic bases, the silanol may be deprotonated by the amine (acid–base). The locally ionized silanol Si–O− groups can now act as a cation exchanger, which is a pretty strong interaction. The reason for seeing the streaking or tailing, as it is called in the formal literature, arises from those dual modes of retention. One mode could be regular partitioning or adsorption and the other
one is this additional cation-exchange behavior.
There are dozens of chromatographic tests for assessing the silanol activity of a given silica gel. Not all silica gels were created equal!
As your question

would that imply that what I'm seeing on the TLC is no longer
pyridine, but rather $\ce{C5H5NH+}$

Remember that ionization is an equilibrium process and hence dynamic. You are seeing the combined effect of both, pyridine and protonated pyridine.