Do you know how THAT worked...did those nations ASK to join?
OTOH...there is absolutely NO upside at all, for US, to join the Commonwealth.OTOH...there would be an upside, for THEM, for us to do so.
No matter how much of an Anglophile Trump is, I highly doubt that he would accept the offer. And the TDS sufferers, as well as many Trumpers would be extremely against him doing so. It could wreck his entire second term, as well as taking down Vance.
Yes; a country that wants to join applies for membership, and the Commonwealth Secretariat reviews the application and hands it over to the Commonwealth Heads of Government for decision.
I don’t doubt that the suggestion might have been made to Trump; I do doubt he would ever take it up.