Colorado

And this is where you lose me. Making things more restrictive is literally the states’ entire job.

No it isn't. The states' job is to create and enforce their own laws that are not explicitly granted to the federal government, nor explicitly prohibited to the States, in the Constitution per the 9th and 10th amendments.

IX The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.

Basically, the Constitution isn't an exhaustive list. If it isn't mentioned, then the default is that the right is retained by the people.

X The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people

Explicitly states that as long as it isn't something explicitly granted to the Feds, or explicitly something the Constitution prohibits the States from (article II, Section 10 gives a list of things that the Constitution explicitly denies the States from having any power in), then the default is that the State controls it.

In this case, the qualifications of members of Congress are explicitly and solely granted to the federal government, through Article I, Section IV.

Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members, and a Majority of each shall constitute a Quorum to do Business; but a smaller Number may adjourn from day to day, and may be authorized to compel the Attendance of absent Members, in such Manner, and under such Penalties as each House may provide.

States themselves do not control Congressional elections. Anyone meeting the Constitutional qualifications (and filed all the correct Federal Election Commission paperwork, HAS to be allowed on the ballot.

And to your broader point, no they cannot just make things more restrictive. The Supremacy clause is explicit in that Federal law and the Constitution overrides ANY state law or restriction that is not what the Constitution itself states. You see state restrictions overturned by the Feds all the time because of this.