The first step In Algebraic-attack is expressing the cipher operations as a system of equations. Is there an automated tool to do this?
Theoretically, the equations could be derived from the representation of the cipher in a hardware description language like VHDL or Verilog; you implement the cipher as if you want to make a FPGA/ASIC which runs it, but you stop at the symbolic representation of the logic gates (the "netlist"). However, I am not aware of any existing conversion tool which will transform a netlist into a sequence of equations in the right format for whatever equation solver you want to use for performing the attack.
Yes, there is an automated tool exists for stream ciphers, and is easily configurable for new ones: https://github.com/msoos/grainofsalt by Mate Soos (great guy, creator of CryptoMiniSAT)
Otherwise, manually but software assisted, people use often Sage for this using this function: https://doc.sagemath.org/html/en/reference/cryptography/sage/crypto/boolean_function.html#sage.crypto.boolean_function.BooleanFunction.algebraic_normal_form and then ANF2CNF by Sage author Martin Albrecht: https://doc.sagemath.org/html/en/reference/sat/sage/sat/converters/polybori.html
CryptoMiniSat (and many other SAT Solvers) "eat" CNF as input.