This question is a mouthful, but I guess I can say that it is easy to say the modern state was not simply the executive committee of the wealthy, but it was pretty close around the time of Marx and Engels. The 19th century was a time of robber barons and runaway capitalism. Historians and journalists like Matthew Josephson argued that robber barons had a complicated legacy of control in the modern state during the 19th century:
more or less knowingly played the leading rôles in an age of industrial revolution. Even their quarrels, intrigues and misadventures (too often treated as merely diverting or picturesque) are part of the mechanism of our history. Under their hands the renovation of our economic life proceeded relentlessly : large-scale production replaced the scattered, decentralized mode of production ; industrial enterprises became more concentrated, more “efficient” technically, and essentially “coöperative,” where they had been purely individualistic and lamentably wasteful. But all this revolutionizing effort is branded with the motive of private gain on the part of the new captains of industry. To organize and exploit the resources of a nation upon a gigantic scale, to regiment its farmers and workers into harmonious corps of producers, and to do this only in the name of an uncontrolled appetite for private profit—here surely is the great inherent contradiction whence so much disaster, outrage and misery has flowed. -Matthey Josephson, The Robber Barons: The Great American Capitalists 1861-1901
There was also the spoils system which is when "a political party, after winning an election, gives government civil service jobs to its supporters, friends (cronyism), and relatives (nepotism) as a reward for working toward victory, and as an incentive to keep working for the party", which got its name based on the phrase from New York Senator William L. Marcy "to the victor belong the spoils". This system allows wealthy individuals to essentially take control of local governments by packing them with their supporters and constituents. This system only ended with the passing of the Pendleton Act in 1883, the same year Karl Marx died.
Eventually, modern governments created more established anti-trust laws, but many of these laws were established after the era of Marx and Engels like the Sherman Act of 1890 & Clayton Act of 1914 in the United States, both of which are considered to be the beginning of modern competition lawbecause older anti-trust laws were not designed to deal with large modern corporations that were able to use trusts to defend their business arrangements as not being 'true' monopolies. So, many could argue that this statement could be seen as true in the era of Marx and Engels.
Now, there are arguments for and against this view in relation to modern times. When it comes to arguments that the modern state only exists to help the bourgeoise, some point to the supposed return of the spoils system in modern politics. Many see redistricting in the United States as a modern return of the spoils system; the fact that according to a 2017 report from Boston Consulting Group, 70% of the nation's wealth was owned by millionaires and billionaires; and growing wealth inequality even during a pandemic as proof of modern states only being tools of the wealthy. However, others many argue against this view, reminding people of the existence of mixed economies with universal healthcare & free college funded with taxes from the bourgeoise; direct democracy in nations like Switzerland, Iceland, and in certain states of the United States which can be used & have been used to fight against corporate interest; & the growth of UBI programs in different parts of the globe to help poorer members of society as proof that modern governments aren't all committees for the bourgeoise. Otherwise, governments would not implement programs and forms of governance that take from their wealth or allow common people to have a say against rich corporate interest.
