Learning new platforms, tools and techniques is inevitable in most careers; in my experience, the first couple of changes are the hardest, and after that it gets easier as you start to link and translate concepts. For some perspective, look at the tools and concepts that existed 20 years ago.
It's better to do it early on (0-10 years), than later in your career (10+ years), when your ideas are more fixed.
To me, the key issue here is the career path you have indicated that you want to follow. There are essentially three choices that most people face along a technical career path: The specialist, the generalist, and leadership.
[I] would like to aim to grow in my career and reach a leadership
position. I currently am not the lead developer, however I am his
"right hand", and get given some of the more important tasks.
Not all people in a highly technical role aspire to leadership positions, and leadership as a skill is quite distinct from any technical skill base. Growing this skill can require as much investment as any technical skill, and in many ways it can be a lot more challenging.
Mobility is important in a leadership role, as most positions have a "life-span" of maybe 2-3 years (initially) and perhaps 3-5 years before you need to move on. The next opportunity may not be within your organisation, and may use different tool sets.
Team leadership is also about putting the overall team productivity ahead of your own; a significant proportion of you time will need to be spent leading, not doing.
I'd actually suggest that going into a team in a leadership role with little knowledge of the platform is a huge advantage.
I found that the two hardest things to learn as a leader were the ability to delegate effectively, and the ability to listen to your team.
If you are an expert in a system, then delegating a task to junior staff is hard. They will do it slowly, and do it wrong. It's frustrating to watch. You want to dive in and do it for them so you can move on.
This is not leadership.
You are not coaching and supporting your staff to improve, you're demotivating them (by making the task look easy) and teaching them that if they give up quickly, you will do their work.
Conversely, one of Covey's "seven habits" is to "seek first to understand, then be understood." If you are going to have to learn from your team about the platform, and how they use it, you will be forced, at first, to listen to them. In doing so, you are more likely to build a rapport with you team, get a measure of their skills, communication styles and productivity.
Understanding your team strengths and weaknesses is important in terms of ensuring they are happy and productive - and of course you are included in that, because as leader, you are still part of the team. Listening and learning from your team is one of the keys to this.
To sum up - if you are interested in a 10+ year leadership career in a technical field, changing platforms as part of a leadership role, in my opinion, offers some significant long term advantages for both development of leadership skills and long term career options.
This was (essentially) my career path over the last 20 or so years.