Page 31 of the Tau codex and page 52 of the core rulebook are the keys to this issue.
On page 31 of the Tau codex, in the Drones box, it says: "Unit Type: As owner." This means that if drones are owned by stealth suits which are jump infantry (jet packs), they are also jump infantry (jet packs).
Page 52 of the rulebook contains the rules for jump infantry. Jet pack infantry is relentless.
Drones that come with stealth suits are relentless and can move and shoot rapid fire or heavy weapons.
Drones that come with XV88s are regular infantry and cannot.