I think if you can make the back-end of the site work with Laravel/PHP it's certainly worth a shot. Most of the time there is no compelling reason to use one back end over the other: it comes down to what the developers are comfortable with and whether it's able to satisfy the requirements of the software, and most of the time all frameworks can meet requirements.
What's particularly important, if the only requirement here is to make a PWA and then a native mobile app, is that current features and functionality of the site can be easily translated to a Laravel/PHP Web app. Again, most of the time Laravel will be suitable unless you have very peculiar requirements.
So what you want to do here is completely separate the functions into back end and front end, so the front end can just drive the back end to achieve something. That way you can use any technology you want as the front end, and native mobile apps are no different here. With good separation, you can just plonk in any new interface you like. If React is a thing, moving to React Native isn't too bad, neither is using React with NativeScript, Ionic or something else.
A lot of the new frameworks revolve around designing more complex front ends. These are usually the JavaScript frameworks and libraries. The Web isn't going away any time soon :) and will continue to be behind most communications and networked technology in the years to come.
If it's ugly to the developers, maybe ask them what they think about Ruby on Rails, Python with Django or Flask, JavaScript and Node, ASP.NET Core, maybe others. It's typically personal preference and experience that drives these decisions, although inheritance of large projects and datasets can play a role. Laravel is very flexible and handles high traffic sites as well as any other, and great sites can be built by talented developers with pretty much any framework. One huge advantage of Laravel is that there are a lot of developers who can use PHP and can pick up Laravel quite easily. You can do a lot with comparatively less effort.
I would focus more on moving the app to maybe an API-based application, completely separating its back and front end components, and what this entails and the special requirements this might bring forward Once that is figured out, it usually turns out that you can use Laravel as a back end just as well as any other, and it can certainly be less expensive (in every sense of the word!) than a huge framework like ASP.NET or something like that. Laravel and PHP are likely to be here to stay given their current age and background, ease of use and number of developers familiar with this technology.