Is assembly implemented only in software with assembler?
Yes. Assembly language is a programming language just like any other, it just uses operation codes that are very close to the instruction set in the processor. It still compiles from a text file that contains source code into machine code that the processor can use.
Who updates and writes assemblers?
Anyone who likes to, from large software companies like MASM from Microsoft, to open source projects like The netwide assembler (NASM).
The companies creating the processors specify the instruction sets, and anyone can write an assembler that compiles to that set.
Is the cpu not even aware that assembly exists?
Exactly. The processor only executes machine code, it can't know if it was created by compiling assembly source code or Visual Basic source code.
If let's say Intel releases a new cpu with added new instructions,
what needs to be done to utilize those new instructions?
You can use them directly in the assembler by just putting the byte codes for the instructions in the code. If you want to use assembly operation codes to use them, those needs to be added in the assembler.