i will write a detailed article on contribution of Assamese Muslims but regarding Bagh Hazarika the fact is that the exact story is not supported by historical documents.. for example Raj Buranji doesn't mention him and in fact no primary sources mention him at all...

in fact we don't find even an indirect mention of him so here are two theories

1. The Story is entirely Fictional and created during some anti-colonial drama (since drama writers were not historians they created entire characters on their own, and made their own pseudo-history, for example dexot koi momai dangor nohoi is entirely fictional, Lachet didn't have any uncle who was fighting in the war.. they just made it up so similarly they might have made up Bagh Hazarika character too)
2. The Story was inspired by some local Muslim hero and got blown out of proportion. This is very much possible because when a community needs an icon to look upto they don't create a fictional hero from scratch but instead just exaggerate an existing icon (bhagwan birsa munda is one example of this). So there might have been an actual local Muslim warrior who fought against the Mughals but they exxagerated certain things such as his position, and added some superhuman touch to hit (such as him defeating tigers barehanded etc)

There were definitely many Muslims in Ahom Army as noted by Mir Jumla who said they ate food together with Ahoms and were more similar to Ahoms than with them. But this particular story of Bagh Hazarika is not supported by hard historical documents. It can be a folktale or an entirely fresh creation by some anti-colonial playwright.. these are my two theories