Osaka had said then she would boycott news conferences to raise awareness of players' mental well-being, but she did speak to reporters after the defeat by Vondrousova.
Two-time champion Andy Murray, whose ranking has slipped to 118 as he battles to come back from hip surgery, will be aiming to win gold for the third Olympics in succession.
Barty used her all-court game, full of all manner of spins and angles, to great effect as she started and finished the match in dominant fashion.
"She's a fighter, a great competitor and she will be sorely missed," Barty, who showed no sign of the hip injury that forced her to retire hurt at the French Open, said on court.
The Japanese government aims to put the new rule, which will be applied to athletes from India, the Maldives, Nepal, Pakistan, Sri Lanka and Afghanistan, into effect on July 1.
The U.S. warnings come just two months before the Tokyo Olympics are set to get under way, something a top Olympic officials last week said would happen even under a state of emergency after being postponed last year.
Federer returned to the courts in March, having been out for more than a year following two knee surgeries, winning his first match in Qatar before losing his second.
The playbook also said all people visiting Japan for the Games were required to have a smartphone and to download two apps for health reporting and contact tracing. Athletes will receive a Samsung smartphone, it said.
"We asked that around 500 nurses be considered," Tokyo 2020 CEO Muto told a news conference. "The main condition is that this must not negatively affect regional medical care."
The organising committee also said it will convene a roundtable with medical experts on Friday to discuss its COVID-19 measures.
Organisers were set to allow 20,000 fans into the May 9 meet, according to Kyodo news agency, but tougher restrictions imposed by the Tokyo city government this month have forced a rethink.