For anyone who hasn't opened it, this quotation from your link Babs explains why Qatar is involved.
The Embassy of Qatar was asked following the Oct. 7 attacks why the country was hosting Hamas leadership.
The Hamas office in Doha … has been used from the beginning as a channel of communication and a means to bring peace to the region and that is in co-ordination with our Western allies, particularly the United States," the embassy responded in a statement.
"When the Hamas office was opened in Qatar several years ago, it was done with the very explicit support of the U.S. and Israel. This was not done against their wishes," Juneau said.