Have Star Trek Online staff made any statements about that?
Yes, in the dev stream last week, a dev said they were asked by Paramount not to have her in Starfleet, there was no reason given. She's just vaguely referred to as 'special ops' in the lore, the new Odyssey Uniform vest variant made for the episode was originally intended for her.
I think they have some kind of vague handwave about the Enterprise-G being retired and the -F returning to service to try and massage the fact that they had the -F being launched 8 years after it appeared on its final flight in PIC.
They haven't acknowledged the story events of Season 3 at all. I don't believe they've referenced Season 2 in lore either. Though the various interdimensional vortices seen in the current storyline are based off the design from the end of Season 2.
If STO isn't using Picard elements, I'd think the more likely explanation is that they just don't have the Picard license. Each series is licensed separately.
No they do. There's various elements from all three seasons in the game, mostly ships, uniforms and weapons.
Very little lore has been adopted, because the series is widely incompatible with their existing lore, but they have been picking and choosing things.
They added the Synth attack on Mars to their backstory, Hugh has made references to the events on the Borg Artifact from Season 1, though in STO's version of events he clearly didn't die. Seven references being part of the Fenris Rangers in one mission.
Seven was already a civilian in STO's lore so that was easy to adapt, however they're using her personality and appearance from Picard, while her previous appearances in STO, which are only a year or two before the 'present', she still looked like and mostly acted like how she did in Voyager, as they came out a few years before Picard aired.
There's been no story references to any events from Seasons 2 or 3 yet.