Which grass, vallisneria ones? You cant bury the crown of the plant but going bit deeper is ok to give it time to root. They should be planted in a small group few cm next to each other. Sagittaria ? Also no burying the crown, should be enough to go 2-3cm deep and 6 cm apart .
Watch this video from this time stamp - see how he plants it in little clumps, the plan is for them to grow and fill in the gaps. Then if one part comes loose it does not take the rest with it as you are seeing now.
I use this method for any plant that keeps floathing up and wont hold in substrate.
Take peace of tootpick or plastic straw place it just under the plant in roots and wrap fishing line or green thread up betwen leaves and under straw to tie it of.
Then when u plant stick tootpick undergravel or sand and anchors plant so it wont float.. Look at my awesome paint skills hahah lol im bored today