Does the expansion of the U.S federal government after 1865 support the argument that U.S civil war itself was about states' rights?

Question: Was the expansion of the U.S federal government after 1865 support the argument that U.S civil war itself was about states' rights?

It's a semantic argument. The civil war was about states rights. For the South it was about their right to keep slavery. For the North the civil war was initially fought over the Southern states right to leave the union. In 1860 the South's slavery "right" was not threatened by the Election of Abraham Lincoln but rather threatened by a political compromise resulting from a generational struggle in the US Senate. The direct threat to the continuation of slavery in 1860, was still years or decades in the future. This threat is what prompted succession, the realization that the South was powerless to maintain its status quo, balance of power in the Senate. This meant, slavery would eventually be abolished, not because of the results of the Presidential election of Nov 1860, but because of a different senatorial bill in 1861 which the South had been delaying for years.

From Abraham Lincoln : The First Inaugural Address (1861)
I have no purpose, directly or indirectly, to interfere with the institution of slavery in the States where it exists. I believe I have no lawful right to do so, and I have no inclination to do so.

Those who nominated and elected me did so with full knowledge that I had made this and many similar declarations and had never recanted them; and more than this, they placed in the platform for my acceptance, and as a law to themselves and to me, the clear and emphatic resolution which I now read:

Resolved, That the maintenance inviolate of the rights of the States, and especially the right of each State to order and control its own domestic institutions according to its own judgment exclusively, is essential to that balance of power on which the perfection and endurance of our political fabric depend; and we denounce the lawless invasion by armed force of the soil of any State or Territory, no matter what pretext, as among the gravest of crimes.

What made the end of slavery inevitable was not Abraham Lincoln's election. It was rather that the majority of the people pushing west were either from the more populous anti slave north or immigrants from anti slave Europe. The Kansas Nebraska act had proclaimed slavery or non slavery for new western states would be decided by popular sovereignty. In 1860 the first states to leave the Union did so because they could no longer ignore what this meant. Their ability to protect slavery would be diluted. That slavery's days were numbered. Without at least equilibrium in the US Senate the south could no longer protect the institution. That is why the more important date for succession than Lincoln's election (Nov 6, 1860), or his inauguration (March 4, 1861) was Kansas's admission to the union as a free state (Jan 29, 1861). That is the event which the South had already fought six years to avoid with their Bleeding Kansas wave of terror. It's an event they had worked to avoid for years in the U.S. Congress. In Jan 1861 they were out of legislative tricks, the vote would occur. This inevitability prompted the first wave of states to leave the union.

• Lincoln's election: Nov 6, 1860

• South Carolina: Dec 20, 1860 (dates of succession)

• Mississippi: Jan 9, 1861

• Florida: Jan 10, 1861

• Alabama: Jan 11, 1861

• Georgia: Jan 19, 1861

• Louisiana: Jan 26, 1861

• The Senate votes for Kansas to enter the Union as a free state: Jan 29, 1861

• Texas: Feb 1, 1861

• Lincoln's Inauguration: Mar 4, 1861

The Union's call for Troops directly from the states, as a reaction to Fort Sumter April 12, 1861, prompted the second wave of succession.

• Virginia: Apr 17, 1861
• Arkansas: May 6, 1861
• North Carolina: May 20, 1861
• Tennessee: Jun 8, 1861

Question #2:
For example, you will encounter a phrase such as "Lincoln ended up promoting a much worse form of slavery - slavery to the state" and something similar to that.

It is true that Lincoln as he stated to Congressman James Alley, "cloaked himself in immense power" during his term in office. He ignored the supreme court. He usurped the powers of congress. He wrote his own budgets, committed the country to debt, and raised an army: all without Congressional input. All these things he did to save the union. Lincoln was the first president to claim war powers. Powers which future presidents admittedly have abused.

Lincoln wasn't the first however to see the need for special war powers. The Roman Republic which the American founding fathers used as a guide had such powers. When the Roman Republic was threatened there was a process where the Senate would elect a temporary Emperor and invest in him all their authority to meet the crisis, with the understanding after the crisis was over this Emperor would lay down his power and the Senate would resume governance. The Roman Emperor Lucius Quinctius Cincinnatus was such a man. George Washington saw himself as a then modern day Cincinnatus. A man given great powers to deal with a crisis, then to set aside those powers in favor of elected legislature. That was very much on George Washington's mind after Cornwallis surrendered at Yorktown (1781). Washington returned to his farm at Mount Vernon. Washington named the post revolution organization of his Revolutionary officers Society of the Cincinnati. America's oldest hereditary organization.

Having said all that I think it's a hard ask to claim Lincoln's branch of history which we endure on today, is worse than historic slavery or akin to a slavery of the state. As George Washington knew, sometimes extraordinary measures must be taken to safeguard a form of government conditioned on compromise and often exempted by stagnation.