Congress is forwarding this impeachment with full knowledge that they cannot remove President Trump from office. That isn't even their stated reason for doing it. The reason that they want to impeach President Trump is to prevent him from running again in 2024. The only problem here is that, since he will not be President Trump at that point, but simply private citizen Trump, Congress doesn't have the power of impeachment.
The framers foresaw the legislature abusing their power. They even included a provision in the Constitution to prevent this exact situation. Article I, Section 9, Clause 3 reads "No Bill of Attainder...shall be passed." What is a bill of attainder?
In British common law, bills of attainder were legislative acts that, without trial, condemned specifically designated persons or groups to death. Bills of attainder also required the “corruption of blood”; that is, they denied to the condemned’s heirs the right to inherit his estate. Bills of pains and penalties, in contrast, singled out designated persons or groups for punishment less than death, such as banishment or disenfranchisement. Many states had enacted both kinds of statutes after the Revolution. The Supreme Court has insisted that “a Bill of Attainder may affect the life of an individual, or may confiscate his property, or may do both,” Fletcher v. Peck (1810).
James Madison said in The Federalist No. 44, “Bills of attainder, ex post facto laws, and laws impairing the obligation of contracts are contrary to the first principles of the social compact and to every principle of sound legislation.”
The Constitution forbade Congress from “exercis[ing] the power and office of judge.” Cummings v. Missouri (1867). In United States v. Brown (1965), the Court specifically rejected a “narrow historical approach” to the clauses and characterized the Framers’ purpose as to prohibit “legislative punishment, of any form or severity, of specifically designated persons or groups.” In Garland (1867), for example, the Supreme Court struck down under the Attainder Clause a congressional statute directed against former Confederates that barred persons from practicing law before United States courts who had, among other things, merely given “encouragement” to rebels.
So if Congress couldn't prevent former Confederates from becoming practicing attorneys, why does THIS Congress feel that they can prevent private citizen Trump from becoming President Trump in 2024?
EDITED TO ADD:
Congress is now trying to pass another Bill of Attainder that specifically prohibits Private Citizen Trump from entering the Capitol.