I'm also reminded of what was said earlier, that you might not be management material given how long you've spent at the role. Now that's something I disagree with to a point, I've found personally, and from talking to people I know within the government sector, that those who are promoted are not always the best fit for the role. In fact, it's often the case that people are promoted because they're unlikely to challenge the person promoting them, there's a high degree of incompetence when it comes to government sector workers. This may be hyperbolic on my end, but it does fit both my experience and that of those I know, including those who have worked within said areas. I'd say the most concerning thing is the fact you've worked there for ten years without looking for work elsewhere, but the fact you're looking now is definitely a positive thing. I'm guessing in your case you simply have not been in the right environment, and a move will do you the world of good.
Look to move under the same role imo, ten years experience is a good thing. Spin it as a positive, but I'd say look for professional advice in this regard, someone that can point you in the direction and tell you how to put a good spin on the fact you've essentially stagnated in the same role for that period. I think if you, as mentioned earlier, move into a similar position in a new place and industry, that you might find yourself much happier, with far more avenues open to you even if you don't want to remain as an admin worker specifically.
