The Dolby Drivers which contain a set of EQ's and compressors on windows are not running and therefore the speakers output's are not calibrated. Best you can do is use pulse's audio EQ for a somewhat similar result but obviously Dolby do not release their secret sauce

Does audio from the headphones sound fine? Are you using ALSA?

Try checking your equalizer and volume settings in alsamixer to see if some alsa settings are affecting your audio quality.

Using Manjaro with the latest kernel and all updates applied.

The built-in speakers sound tinny and bassless. Are there drivers or settings that can help with the quality of the sound output?

Cheers.

Audio from speakers is tinny and bassless