I am no professional but if I were you I would speak to the HR advisor again. Your current manager is new and not aware of the history and your previous managers behaviour will be recognised with the HR advisor.
In terms of whether the role should have been advertised internally, you need to check the recruitment policy to see.
"if she turns down my request to be seconded into her team- would I be able to raise a grievance about the initial behaviour?"
Presumably you are not entitled to be seconded, and managers can turn down requests? Again that's an internal policy question.
But no, you can't raise a grievance about something that happened 2.5 years ago if someone makes a decision you don't like now. Well, you can, because you can raise a grievance about whatever you like, but it would not be seen as reasonable, particularly as you were specifically asked if you wanted to raise a grievance at the time and said no.
When was the last time you proactively contacted the manager in question? If you had a productive chat 9 months ago and she was supposed to email you back but didn't, presumably you didn't just leave it 9 months and not do anything? Have you taken any action in that time to move things along?
Can you have a chat with HR without raising a grievance (bit late now), and just say you're thinking of applying for this role involving the manager they know there's history with, and would like it to go smoothly, can they help you do it by the book?
This may have the twin merits of making sure you don't give openings for unpleasant manager to turn you down, and of flagging the potential for problems to HR before things go pear-shaped, rather than looking like a bad loser afterwards.
But most of those things happened more than 2 years ago, yes? The only recent thing you could legitimately complain about now her is not picking up something after a meeting 9 months ago. And you say you haven't chased her or taken the initiative at all. I'm just trying to put across how your employer will see it/respond if you start talking complaints and grievances at this point.
I think Surely's advice is excellent, and the way to go, although based on your last post I would also recommend reconsidering this plan completely....