Upon logging out and back in, I found all my cargo to be gone through some other bug, but (despite build mode stats not indicating it) my ship kept all its extra mass in cargo. Given the current placeholder cargo config, this rendered the ship essentially immovable.
(May be related to T922 or a similar issue)
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When a stack gets dropped by the "bleed when over capacity" mechanic, the added mass of that stack doesn't get removed from the ship or if it does, not completely. The GUI shows there's no added mass but at least the ship still acts like that.