No, Phandelver & Below does not contain anything from Dragons of Stormwreck Isle or Dragons of Icespire Peak at all.
Phandelver & Below is essentially two different adventures:
1. A re-print of Lost Mine of Phandelver with changes that make a great starting adventure mostly worse. For example, Cragmaw Cave (the first dungeon, for level 1 characters) is already slightly too deadly in the original version. Well, they added way more enemies and made it much harder in this version.
2. Another, totally new adventure which is nominally a sequel to Lost Mine but really doesn't pick up or expand upon anything from Lost Mine, but instead just presents a level 5-11 adventure which also happens to be set in and around Phandalin. NPCs who appear earlier in the book who were changed and re-named from the original LMoP revert back to their original LMoP names here the second half because sloppy editing. Adventure consists of a series of dungeons (some good, some mediocre) and a nonsense villain plot. Best for groups that want to kill things in dungeons and not think too hard about why anything is happening. Also, editing mistakes.