Failed to convert a NumPy array to a Tensor (Unsupported object type numpy.ndarray) - Already have converted the data to numpy array

There are three problems

problem1
This is your main problem, which directly caused the error.
something's wrong with how you initialize/convert your x_train (and I think it is a bug, or you used some unusual way to construct your data), now your x_train is in fact an array of array, instead of a multi-dimensional array. So TensorFlow "thought" you have a 1D array according to its shape, which is not what you want. the solution is to reconstruct the array before sending to fit():

x_train = np.array([np.array(val) for val in x_train])

problem2
Dense layer expects your input to have shape (batch_size, ..., input_dim), which means your last dimension of x_train must equal to input_dim, but you have 300, which is different from 400.
According to your description, your input dimension, which is the word vector dimension is 300, so you should change input_dim to 300:

model.add(Dense(20, input_dim=300, kernel_initializer='he_uniform', activation='relu'))

or equivalently, directly provide input_shape instead

model.add(Dense(20, input_shape=(400, 300), kernel_initializer='he_uniform', activation='relu'))

problem3
because dense, aka linear layer, is meant for "linear" input, so it expects each of its data to be a vector of one dimensional, so input is usually like (batch_size, vector_length). When dense receive an input of dimension > 2 (you got 3 dimensions), it will perform Dense operation on the last dimension. quote from TensorFlow official documentation:

Note: If the input to the layer has a rank greater than 2, then Dense computes the dot product between the inputs and the kernel along the last axis of the inputs and axis 1 of the kernel (using tf.tensordot). For example, if input has dimensions (batch_size, d0, d1), then we create a kernel with shape (d1, units), and the kernel operates along axis 2 of the input, on every sub-tensor of shape (1, 1, d1) (there are batch_size * d0 such sub-tensors). The output in this case will have shape (batch_size, d0, units).

This means your y should have shape (462, 400, 9) instead. which is most likely not what you are looking for (if this is indeed what you are looking for, code in problem1&2 should have solved your problem).

if you are looking for performing dense on the whole 400x300 matrix, you need to first flatten to a one-dimensional vector, like this:

x_train = np.array([np.array(val) for val in x_train])  # reconstruct
model= Sequential()
model.add(Flatten(input_shape=(400, 300)))
model.add(Dense(20, kernel_initializer='he_uniform', activation='relu'))
model.add(Dense(9, activation='sigmoid'))
model.compile(loss='binary_crossentropy', optimizer='adam')

model.fit(x_train, y_train, verbose=0, epochs=100)

now the output will be (462, 9)