Consumer audio products like the "sound bars" you mentioned are made for applications where precise timing is less important. Whether there's a 2.5 ms or a 25 ms delay between the input and the output isn't really important for music playback or even TV.
These products often combine analog and digital audio sources, and the easiest way to add e.g. equalization to the sound is to convert all sources to digital, then do all the processing in the digital domain, and then convert to analog again.
Conversion and digital processing inevitably adds a time delay, and if the product is not specifically aimed at musicians, minimizing this delay may not have been of prime concern during the design of the product.
What you need to amplify an instrument is either an amplifier specifically designed for that purpose, whether analog or digital, or a consumer audio product that is completely analog (for which you may have to go second-hand and probably pre-21st century). The people I know who play electronic drumsets all use either a dedicated e-drum amp, or a keyboard amp.