The monarch is the custodian of our unwritten constitution. Though not codified, the UK's constitution is written in hundreds of Acts of Parliament, court cases, and in documented conventions. Its essential principles are Parliamentary sovereignty, the rule of law, democracy and so on.
Right now the Conservatives have a healthy Parliamentary majority and don't need to go the polls for another two years. Larry the Downing Street cat could be PM if the governing party wished it so and Charlie boy would have no say in the matter.
I believe Truss is finished, but the mechanics of her downfall will only emerge once the political arm wrestling between the various factions in the Conservative Parliamentary Party ends. Once that's resolved, a mechanism will be set up to remove her and replace her.
When Johnson was ousted it wasn't a constitutional crisis and removing Truss won't be either, they'll just have to tear up the Tory rule book for this one but that's no business of Charlie boy.