The source impedance, ##R_l##, isn't used anywhere, except in the schematic. So I suppose we can assume it's zero? It, and the source transformation mentioned, seem irrelevant.
Series resonance and parallel resonance are fundamentally different topologies. But, if you restrict your analysis to any single frequency, resonance in this case, you can pretend they are the same. They both have a quadratic term (high Q) somewhere in their factored pole-zero response (impedance, transfer function, etc.).
The canonical form of this term will be ##[1 + (\frac{1}{Q})(\frac{s}{\omega_o}) + (\frac{s}{\omega_o})^2 ]## for ##Q>\frac{1}{2}##
With the associated definitions:
## s = j \omega ## , for steady state or single frequency analysis. s is the Laplace variable used in transient analysis.
## \omega_o = \frac{1}{ \sqrt{LC}} ## , the resonant frequency.
## Zc=\sqrt{\frac{L}{C}} ## , the characteristic impedance.
## Q=\frac{Zc}{R} ## , for series resonance, or ## Q=\frac{R}{Zc} ## , for parallel resonance
Personally, I always found this format easy to remember. It may be worth memorizing.
For example,
The impedance of a series RLC branch is ##Z(s)=sL + R +\frac{1}{sC} = \frac{s^2LC+sRC+1}{sC}##
The admittance of a parallel RLC section is ##Y(s)=sC + \frac{1}{R} +\frac{1}{sL} = \frac{s^2LC+s\frac{L}{R}+1}{sL}##
I doubt that there is any physical significance, it's just that there are useful similarities in the math. There are about a million ways that EEs talk about resonance, if you don't like this approach there are many others on the web. Many are pretty sloppy with underlying assumptions. I prefer to go back to the math, personally.
You may also be interested in exploring the idea of dual circuits. These are different topologically but have the same solutions under a set of duality transformations, which, of course, is applicable here too.
https://www.ams.org/publicoutreach/feature-column/fc-2019-05
PS: Also note that at resonance ##\frac{s}{\omega_o} = j##, which makes the math easy.