Could impeachment and censure of a US president for the same set of issues proceed independently, either roughly concurrently, or sequentially?
There’s no procedural reason why not, but there is a practical one: censure would be a far lesser punishment than impeachment. For the same people to argue for both impeachment and censure at the same time for the same reasons would undermine their own argument that impeachment is the appropriate remedy for whatever malfeasance that they seek to punish.
To argue for impeachment and censure at the same time is to say, simultaneously, that you think the President did something so bad that it is worthy of removal from office, and that exact same thing the President did is bad but is not worthy of removal from office.
Those two premises are contradictory. The natural way for people opposed to impeachment to resolve the contradiction is to point out that if censure is an adequate remedy then impeachment is unnecessary and excessive. The natural way to for people opposed to censure to resolve that contradiction is to argue that impeachment is the appropriate remedy. The natural way for people opposed to both (e.g. Republicans in Congress) is to simply point out that the contradiction is proof that Democrats don’t really know what they want to do, and then subsequently argue that the indecision happened because these impeachment hearings are not a serious attempt at addressing misconduct, but simply an attempt to slap Donald Trump with anything that sticks. The Democrats are fully aware of that particular counter-argument, which is why there is pressure in their caucus to pick one remedy (e.g. impeachment) and discourage pursuit of the other (e.g censure).
So, yes, Congress could do both at the same time, but it would undermine achieving both goals and therefore be self-defeating.