Doesn't antenna length have more to do with wavelength of the signal? Longer antenna for longer wavelength, as for 2G. Shorter antenna for shorter wavelength, as for 5G. A higher antenna, e.g. mounted on top of your rig, is better than a ground level antenna, whether 2G or 5G, whether a long antenna or short antenna.
Correct me where I missed the mark. I'm still learning.
In general terms antenna length is, indeed, related to wavelength as you describe. However the key takeaway here is that this is speaking of electrical length, not physical length, because different materials will have a different speed of propagation (speed of light, sorta), thus the physical length will be different in iron than in copper, etc. Antenna configuration also plays an important role, such as dipole vs quarter wave vertical vs loop, etc. And finally, for example, a nominally 9 ft. antenna (CB, 27 MHz) can actually physically be 3-5 ft if coils, etc. are configured to add to the electrical length to bring it up to the required 9 ft. (all figures approximate).
The above isn't a complete explanation, but should be enough to get the idea that there are many ways to compensate for the need to fit an antenna into a reduced space (of course performance suffers to some degree).
Height IS king, though, and you have that right, BUT, only with the right feedline setup and being in the clear (not behind metal, etc.)
Turn the amp off and you still get 3 bars. Is it the weak antenna or the height of the antenna?
Could be either, depending on the exact configuration. And don't expect "bars" to be a linear indication of signal strength -- generally more bars is "better" but multipath and other interference can affect (degrade) actual performance in surprising ways. Radio wave propagation is extremely complex, weird, and differs with frequency as well.