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Two options. First, the cartridge may have a Schrader valve on the top underneath the saddle clamp. Stick a shock pump on it and check the pressure is good. Second option is it's a sealed cartridge, which you should be able to replace. Brand X (Trans-x) make dropper posts for a lot of brands, so the cartridge might be searchable under another name. You might have to pull out the cartridge to get the code before finding the correct replacement though.
Brand x ascent dropper post. Came used with a mountain bike I bought; it goes up and down, but when I sit on the saddle in the locked out position, it bounces, much like a suspension fork/front shock.
Googling around it seems the consensus is that it isn't user serviceable and it's off to landfill especially since I can't return it under warranty.
https://photos.app.goo.gl/WF4J9urP3z4HmVBe7
video of the squish in action. suggestions of what to do outside of buying a new product and throwing this one in the bin welcome.