There are quite a few ways to approach this. First, you really need to figure out whether this is actually worth doing. Run a survey with your users and ask: would they be genuinely happy to have native mobile apps?
If the feedback is positive and the dev team decides it's worth investing the time, then you can choose the tech stack — either Flutter or native iOS/Android development. That decision can be made by a quick team vote or based on the real expertise of the people who’ll actually be building it.
Put together a small team: a project manager, a designer, and a couple of developers. Build an MVP and start rolling it out. Of course, there’s always a risk it won’t work out.
But honestly, I think the first step should be running that user survey. If only 1-10% of people say they want a mobile version, then it probably doesn’t make sense to do it at all.