This kind of promotion, the tweets, the events attendances, and the link on her official website are contractual, in my opinion. It’s clearly not what you do when you’re in a relationship, especially when you’re not out yet. Long time official couples can promote each other’s works, no one is surprised when Beyonce promotes Jay Z’ albums (that’s the first example I had in mind, sorry) because they’re out, official, married and have a child. But there are rules to follow in this industry, either you’re a big worldwide celebrity or not. First, you come out. Then you promote your partner. Gillian promoted The Crown even before we heard about PM. She keeps hanging out with him, yet, nothing has been confirmed about their supposed relationship. To me, it just means there’s no relationship at all, only a work partnership. I think she’s more involved with the show than with him because everything they’ve done together was about it.
That said, I also think she’d made a PR mistake, or was badly advised. Because if she’s dating him, she’ll be accused to have over-promoted his show, even more than her own projects, people already have a bad opinion on him and will take him and their couple responsible for pushing xf back, and it can be seen as a bad move from a major part of her fandom. If she’s not dating him and will be involved in The Crown, she needs to clarify the situation before it’s announced or we all know what she’ll be accused to. I bet her involvement in The Crown will be announced in the next few months, when the green light for the third season is official, but before that, she’ll make a random interview when a journalist will ask her directly or not, and she’ll make it clear that she’s not and has never been dating him. That’s how I see it… We’ll see…