I've only just seen it but I'm not sure why people are conflating a piece of film taken in London with anything at Sandringham. Kate is hardly the only VIP who would get protection in the UK.
Yes, accept William ducking out of the memorial service at the last moment was odd and has certainly fuelled speculation about Kate (some funny, some completely bonkers) However, we are a month from Easter and nothing has changed in terms of the timescale for her return to public life. It isn't as if it is now November and she's not been seen.
Even in the lowly world of local government there is generous sick leave to allow for recovery from surgery and employees there aren't expected to issue statements or send videos of them working from bed to their bosses. In her place, with the extra pressure of having to look bloody perfect all the time, I'd be v low profile too.