The Watchers Council (apparently) weren't informed. The Scoobies resurrected the Buffybot and used it to impersonate the real Buffy for several months. Her relationship with the Council was so choppy at this point that there was little chance of the ruse being uncovered if Giles didn't tell them.
GILES: We just can't have her messing up in front of the wrong person -- or
the wrong thing. We need the world and the underworld -- to believe Buffy is alive and well.
Bargaining: PtI - Original Screenplay
Note that Buffy's death didn't result in the calling of a new Slayer (which would have immediately alerted the Watchers) as hers was no longer the "active line".
New Vampire Slayer Wanted? by Charlie Mason
Where's the Watchers Council when you need it? Historically, every time that one Slayer is killed on Buffy the Vampire Slayer, another is magically drafted for active duty. Heck, back in the first season, Buffy (Sarah Michelle Gellar) only stopped breathing for a matter of seconds before a successor, Kendra (Bianca Lawson), was dispatched to Sunnydale. So, after Buffy spent the entire summer pushing up daisies, how come no new Slayer has been called to arms? Has the show forgotten its own mythology?
"We actually have an answer for that," executive producer Marti Noxon tells TV Guide Online. "It's a technicality. The reason [Buffy's demise didn't activate another vampire hunter] is that when she died the first time, a Slayer was called, so she's already had her replacement Slayer.
"It doesn't happen twice," she continues. "You only get one, and Buffy already did."
The fact that Kendra quickly kicked the bucket, and her next-in-line, Faith (Eliza Dushku), is behind bars makes no difference to the powers that be. "Since Faith is still alive," Noxon notes, "the line remains intact."
So, in other words, viewers shouldn't look for another stake-toting teenager to turn up in Sunnydale anytime soon "” at least not unless Dushku's burgeoning film career takes a dive. "It would take Faith dying for another Slayer to be called," Noxon says, "and since we can't get [Dushku] on the show, the odds of that happening aren't big."
Buffyboards.com quoting TV Guide
For the record, everyone seems to have had a really crappy summer and nearly gotten themselves killed a bunch of times but there's no mention of a 'big bad' turning up that they had to deal with, just the usual run of vampires and demons. They got lucky.