For fermentation in general, let me give you a few tips that may be tripping you up:
Don't wash ANYTHING in chlorinated water before going in the jar.
The salt type and granule size is very important.
Always calculate salt by total weight of the jar + contents
NEVER add chlorinated water to the vessel. NEVER EVER EVER
Some tips for Kimchi specifically:
Smash the garlic and let it sit for a few minutes before chopping or adding
Get the finest granule of pepper "flakes". Not the large flake kind meant for soups or stews. You want powder, practically. Deep red, and about the grain of table salt at max.
Mix your salt, sugar, pepper flakes, garlic and onion FIRST before adding them to your cabbage. A little bit of soy sauce or spring water for moisture. Let the mixture sit a good 30m to bloom before rubbing into the cabbage.
RUB THAT MIX ALLLLLL OVER EVERRRRRYTHING. When I say everything, that means every little nook and cranny of the cabbage. Squeeze the cabbage a bit while doing so to help release some moisture into the marinade.
Get a muddler to help smash and bruise the cabbage as it's going into your jar. You really want it packed tight, and smashing it as you go releases even more moisture into the mix, so by the time you've filled the jar, you should have enough volume to mostly cover the top
Get some weights for the top to make sure the last bits added are submerged.
It's really not too bad. You just need to get all the ingredients together and follow the steps. Cucumber kimchi is my favorite and pretty easy to make.
I've made kimchi before, but under the supervision of my mom. So I'm not exactly an expert.
To me it looks like your kimchi is too watery. After looking at the recipe I think I may know why. This is a vegan recipe, traditional kimchi not only has fish sauce, but it also has quite a bit of fermented shrimp brine.
It doesn't look like the recipe you linked has enough salt in the actual spice mix, traditional kimchi gets this from the shrimp. If you don't have enough salt, the marinade won't fully saturate the cabbage.
If you are trying to do a traditional vegan recipe I would suggest just doing This but substituting salt for the shrimp, and something like tamari or something with umami for the fish sauce.
I actually don't know if I would use that recipe, it seems low on both sugar and salt for preservation.