Shannon-Nyquist - only for repeating signals?
if you decompose a signal into sinusoids, and then sample at 2x the highest frequency sinusoid, you can perfectly reproduce the original signal.

If the signal can be perfectly decomposed into sinusoids, then by definition, the signal is bandlimited to the frequency of the highest one, and Nyquist applies.
This applies whether the signal is continuous or sampled, as long as we keep our assumptions about the sampling consistent.
If we just have a bunch of uniformly taken samples, and no further information, then we don't have enough information to reconstruct a unique signal from which those samples were taken. We need to make an assumption about which alias was being used. Usually, we make the simplest assumption that the first (or should it be zeroth?) alias was sampled, and the signal has frequencies in the range DC to sample_rate/2.
Often, especially with high IF software defined ratios, a higher alias is sampled, and the signal has frequencies from fs/2 to fs, or even fs to 3fs/2.
If you have a perfect triangle wave, or a square wave, then you have frequencies going to infinity, and your 'if I can decompose ...' condition is false. Once bandlimited, a square or triangle wave looks rounded, and maybe gains overshoots, depending on the group delay of the filter used to remove the high frequency components.