It's the same old story again: some T&M gear - an AWG in this case, that costs next to nothing, yet it has to be "decent" nonetheless.
"Decent" in this case appears to be "80-100mHz". I very much doubt this. I suspect it should rather be 80 - 100 MHz. Is it really too much asked to use correct terminology in an EE-forum? "m" = milli, "M" = Mega.
These 80 to 100 MHz apply to sine waves. Of course square and triangular waves have much lower frequency limits. A 100 MHz AWG has to have a 100 MHz reconstruction filter (ideally brickwall) at its output(s). Guess what happens if we tried to output e.g. a 50 MHz square under those conditions. Of course it would be a pure sine.
So it's up to the manaufacturer, how much deviation from the ideal waveform they think the customer will be tolerating. They'd have to limit the square wave output to max. 20 MHz in a 100 MHz AWG, in order to include at least the 5th harmonic, thus getting sort of barely acceptable signal fidelity. Yes, there are rare exceptions, like the Siglent SDG1000X series, which have a dedicated circuit for square wave output - but that's quite some effort, rarely seen anywhere else and even in the higher class AWGs from Siglent, because while it's easy to convert a sine to a square by means of a comparator, it's not so straight forward to recover the amplitude.
It is similar with triangular waves. What amount of nonlinearity are we willing to tolerate? 1 %, 2 %, 5 %...? The whole reason to have triangular waves (and ramps) traditionally was for linearity tests. That's why we cannot tolerate high non-linearities, hence triangular waves and ramps are limited to low frequencies - usually 1 MHz or even lower. On the other hand - what would be the use of a high frequency triangle wave?
The above hints apply to quality gear. Some manufacturers might not bother and present you quare waves that are almost indistinguishable from sines and you get heavily bent triangular waves. Yes, the user still has the option to limit the use of those waveforms to lower frequencies, but the fact remains that inexperienced users might get fooled by the false claims in the specs of such products.