No, that is currently not supported and is not being worked on. It is planned though. Videos showing up as embedded content in posts should be available on some Lemmy clients if the link is a direct link to a video file (I think Liftoff has that 🤔). Regarding uploading videos directly on your instance, even if that is implemented (which is planned), very few instances will actually allow that. Video just takes way too much space, and recoding it takes way too much CPU/GPU power, considering how many users a single instance can have. Heck, many instances have even resorted to either using imgbb or another free hosting service to hold images instead of their instance, or limited uploads of image files to an avatar size only (100KB). Media just takes way too much space. Recompression and recoding solves that problem partially, but as noted, it takes way too much CPU/GPU cycles. Most instances are either selfhosted or through a VPS. Things like that cost money and I doubt the donations are big enough to also leave room for server upgrades or upgrading the payment plan for the VPS.

So, even if it does happen, don’t hold your breath that your instance will enable this by default. My guess is that most large (public) instances will have this feature disabled by default. Smaller private instances (instances for friends and family only) will have this feature eanbled, but you can’t register an account on those, so 🤷.