This is the question owners ask most and the one nobody has answered properly, so here is exactly where the evidence stands and what we are willing to say.
DJI publishes nothing. Not on whether a filter and the wide-angle lens can be mounted at the same time, and not on whether the gimbal retracts and the protective cover closes with a filter attached. The manual gives the filter and the lens separate storage slots inside the cover, which is a hint and is not a compatibility statement.
The sellers answer it, and they disagree. One brand prints do not stack filters and lenses, and remove the lens before turning off the camera. Another says its filters are gimbal-friendly and compatible with the gimbal. A third claims its thinner glass fixes a problem with DJI's own filters obstructing the camera locking in, which is an accusation against the first-party part that DJI has never addressed. A fourth, writing about a different Pocket generation, says flatly that stacking will damage the gimbal.
Owners report brand-specific outcomes. An owner of the variable set advertised as gimbal-friendly reports the gimbal cannot close with any of those filters attached. In the dedicated stacking thread, one owner stacks two filters from one brand successfully but has to remove them before powering down, and another reports that filters from different brands do not stack because the magnets sit in different places.
What we will say. Filters mount, and that is not in dispute. No stacking claim on this camera is verifiable, and nothing about gimbal closure has a source stronger than a seller bullet or a single owner. If you buy on the basis that you can leave a filter on and shut the camera in its cover, you are relying on a claim no manufacturer has stood behind. Take the filter off before you power down and none of this matters.