Yes, you do. You always maintain diplomatic channels. It costs you nothing (of significance).

Diplomatic channels, yes. Head-of-state summits, no.

You don't need to invite Putin to U.S. soil for a one-on-one meeting with the POTUS. Both the U.S. and Russia have each have an entire foreign ministry full of people who maintain diplomatic channels. You shouldn't do a summit if you're trying to diplomatically isolate the country as a way of using every possible pain point to force them to stop the fighting in Ukraine.

Right - they’re complete unaware of the fact that Russia is a pariah state and that many of them have been personally sanctioned by the west. The red carpet and the foie gras were totally more relevant to them.

Every television and newspaper in the country is going to run photos of Putin shaking hands with the U.S. President, who rolled out a literal red carpet for him and stood by his side while letting him have an open mike at the press conference. Putin will have all he needs to tell the story that "yes, the wimps in Europe are all crazy about this - but the countries that really matter don't really think this is that bad. How much of a pariah state can we be if the President of the United States is rolling out the red carpet for me?" It's a gift to Putin and his ability to argue that sentiments against his country aren't as extreme as anti-war folks make out to be, or might be permanently damaging.