Welcome to the forum Javier.
Personally I would keep them separate. Reason being, if one breaks down the replacement cost isn’t as much, and it’s easier to troubleshoot something that is less complex. I’ve also found that “all in one” devices tend to not be as reliable as standalone devices, especially if it’s low cost - there has to be a tradeoff. The company making controllers may not make the best inverters, and vice-versa.
Also, keeping them separate may give you more flexibility in the design, and is more able to adapt to your changing needs. I almost never use an inverter. Almost everything I have runs on 12 volts, which is much more efficient than running things on AC. If you run everything on AC (220 volts), you’ll need more battery and charging capacity, which drives up the cost and adds to the complexity. More likely to not work when you need it the most.