While there's always room for more discussion, you might be interested in my answer to Was a perpetrator of the 1804 Haitian Massacre really the inspiration for the Zombie horror trope?.

Cultural expressions of anxiety are difficult to diagnose in strict terms of historical evidence. Certainly, several writers on the subject have interpreted the specific image of the zombie as an individual enslaved to another after death as being a horror particular to a people that knew slavery in life. The idea that death was no escape from such servitude would seem fitting.

However, the actual evidence on the ground is a little more complicated. The term zombi as we know it did not originally refer to an animated corpse, but was a term for a spirit, god, and/or fetish, and can be compared to similiar West Indian terms like jumbee. Even today, the term can have multiple meanings in Haitian vodou. Ackermann and Gauthier in "The Ways and Nature of the Zombi" have a table of possible etymologies, including fumbi (spirit, Yoruba), mvumbi (cataleptic individual/invisible part of man, Yoruba), ndzumbi (corpse, Mitsogho), nsumbi (devil, Mitsogho), nvumbi (body without a soul, Mitsogho), nzambi (spirit of a dead person, Kongo), zam bibi (night bogey, Ewe, Mina), zumbi (revenant, Bonda*, zumbi (fetish, KiKonga), zemi (spirit, Arawak), etc.

In Haitian Vodou, there is a concept of a dual soul: the Gros Bon Ange and the Ti Bon Ange; the exact details as to which is the target of sorcery or leaves the body during sleep, possession, and death varies depending on which writer you're reading. By the same token, "zombis" themselves are confusing, often referring to either a soulless body (one in which either of the dual souls has fled), or a bodiless spirit...and if you dig deep enough, you get "zombies" that don't really fit either category. The distinction is sometimes explicit (a corps cadavre is a soulless body), but it can be difficult to really nail things down in folktales.

There are indigenous African traditions which contain corps cadavre-like figures, such as the Tanzanian zinza, where a dead body missing one of its souls is made to do manual work for a witch or sorcerer, but pinpointing the exact origins of such traditions - or equating them directly with Haitian Vodou - is a tricky proposition at best. Generations of separate development and syncretism have created a bit of a muddle.

Which gets us back to your initial question: is this an expression of cultural anxiety? In Haiti in particular, the role of slavery and the bloody revolution (and subsequent political turmoil, wars, invasion and occupation by US forces, etc.) have made knowledge of the horrors of slavery an essential part of the Haitian culture. To some researchers, like Maximilien Laroche, this certainly suggests that the physical zombie acting as a slave is a symbol of the continued horrors of sorcery. But the nature of what exactly a zombie is remains too vague and sometimes contradictory to say that is the only explanation.

In later media, the slavery aspect is very strong, especially given the racial dynamics of slavery in North America. The first zombie film for example was White Zombie (1932), loosely based on William Seabrook's The Magic Island (1929), and focuses on the dynamics of white people being enslaved just like native (black) Haitians by magic.