Like others, I typically play an entire album start-to-finish and have any media iCloud Library syncing options disabled on my iDevices and iTunes respectively.
Additionally, I typically drag-n-drop albums via the iTunes (Mac and/or Windows) interface after physically connecting my iDevice via USB. This approach yields individual tracks as albums. Using the "Add To Library" option in iTunes and then drag-n-dropping from the iTunes Library to the iDevice instead yields the desired result on the iDevice - still doesn't solve the problem introduced as of watchOS 6.1.
That said ..
*UPDATE*
Created a "test" playlist on the iPhone (8 /w iOS 13.3) and added an entire album to it. Selecting the playlist on the iWatch (S5 /w watchOS 6.1.1) plays the content of the "test" playlist as expected.
Also took a moment to compare the "Song Info" properties via iTunes of a track on the iPhone against the Library version; visually, the track metadata appears consistent.