According to this video stars at end of time and many others on fate of universe they all agree on one thing that stars will eventually convert all the hydrogen into heavier elements and eventually there will be no light , i understand the documentaries are over simplified but is it really the case that universe had/has finite amount of hydrogen to start with and there is no known process that recycling hydrogen back into universe
Are you sure it's true that all hydrogen will eventually be processed? I can see that star formation rate should eventually slow to a point that there would be essentially no more light being created, but that's not the same thing. Right now, most of the hydrogen in the universe is in the space within clusters of galaxies, and some of it falls into galaxies and some gets ejected, so you might imagine that all of that will eventually get processed. But there is also hydrogen in between galaxy clusters, in the "cosmic web", and since the universe is expanding quite rapidly, it seems quite possible to me that much or most of that gas will never fall into a galaxy, but instead just end up stranded in between the expanding clusters.
What's more, our models now include the "cosmological principle" that treats the universe as homogeneous, but that's just the universe we can see. We have good evidence that it extends way beyond what we can see, so we have no way to know (or even to expect) that the homogeneity is a truly global property of the entire universe (i.e., not just the "observable" universe). On scales we cannot probe, the structure might be fractal, meaning that there could be pockets somewhere doing very different things, and there might always be stars forming somewhere. Another possibility is that there could be a "landscape" of universes, which is hard to say if they count as the same universe or completely different ones, but it does mean there could be in existence hydrogen elsewhere in the "landscape" even after our universe has none. So it's a tricky question to answer if "all the hydrogen" will eventually be processed, but I suppose you could look at all the hydrogen in the observable universe-- but you still have to wonder if the gas between the clusters ever gets into a galaxy.