By manually adjusting the level upwards for the softer parts you are doing a form of manually applied bottom-up compression. It's actually quite similar in a lot of ways, although there are differences- if those differences are good or bad depends on how you look at it. Some of the differences are sonic, others are more about how you go about doing it and the time required to do so.
Manually drawing level changes and crossfades gives you specific control over each section- exactly how much each part is boosted and how it blends into the surrounding louder sections.. and that requires specific attention to getting the level and fades set for each section. With enough attention to the crossfades, doing it manually it might be less prone to introducing sonic artifacts than using a compressor plugin, parallel or otherwise. Some of the potential artifacts I notice are the pumping, or audible modulation of lower level constant background noise in the quiet sections: things like guitar amp hum, HVAC rumble, etc. Setting up parallel compression takes more time initially to dial in the right settings to avoid those problems, but doesn't require applying it individually to every quiet part.
So then one practical question is how ‘granular’ you want to get in your dynamic level adjustments. If there are not very many, you may want the extra control of doing it manually. Then again, if applied automatically as determined by the level of the recording itself, the compression might be more consistent across all sections, even very short segments. If you slice the pie in small enough pieces, you’d go nuts trying to envelope them all.
Sonically a few things are different as well and again, if those are good or bad, depends. Parallel compression effects the microdynamics within the quieter sections as well as the overall macrodynamic level of the entire section. It evens-out the level of sounds within those soft parts, bringing up the background sounds more than just raising the overall level by the same amount would. For highly transient material which doesn’t have a high average level, it sort of thickens things up. That can often be heard on drum sections, were it compresses and brings out the lower level trailing resonances after the brief, high-level hit peaks. In mixing, it’s sometimes applied the drum buss for that reason
Also as mentioned previously, it's a common approach to EQ the compressed copy differently from the uncompressed copy, which has the effect of applying a different EQ curve to the quiet parts verses the loud parts. Like you, I haven’t put much time into mastery of the DAW interface and complexities either. My DAW allows automation of EQ curves so I could manually adjust EQ over time similar to drawing in manual level changes, but I’ve never figured out how to do that.. and it would probably take me way too much time to adjust it all to my satisfaction.