Yes. Bungie was an independent studio back in the 90's, then MS acquired them for Halo. Bungie split from MS in 2007; the Halo IP remained behind under 343.
They were under Activision during the Destiny era until 2019. So if they stayed, they would've ended up back at MS. The M&A merry-go-round continues.
They weren't under Activision, they just had a publishing agreement with Activision in the 2010s, and retained all intellectual property.
Hm, surely it must have been later than 2007 that they split? Wasn't Reach made by Bungie?
They split in 2007. MS then had them make reach as an independent company.
When they announced the split in 2007, there was some deal that required Bungie to make two more Halo games after 3. Bungie released ODST in 2009 and Reach in 2010.