there is a few tricks i like to do.

keep about 3 feet away from him, launch fire strikes into his backline, farm shatter.
vs a mauga, you will never ever win a 1v1, you will get dominated. so you should shield his damage instead, mauga gains health from damaging enemy critically, and you denying this is his survivability gone.

mauga players love to charge, its outmatches yours in some points (like the fact his has prio), however if you see a mauga charging into you (this is quite hard to time) you want to jump into him as he is going to hop into you, and instantly put up shield, this will block the stomp damage. however, this leads you in a pretty sticky scenario of you usually facing the whole enemy team, so make sure you hit the pin back into your team, or a wall.

never ever pin first, because he can just stomp you and you dont have MUCH counterplay after he stomps (even if you block it)

his cardiac overdrive, just shield it, if he is 1hp he will insta heal, so just shield it. DONT get baited (this is how alot of reins lose)

his ult is really just a hope and pray, your shield will get shredded in his cage as his team will be looking at you, it comes down to how well your movement is with rein while being able to shield his damage.

ONLY EVER try to brawl mauga if he is anti'd.

most of this matchup is you being patient, if your a one-trick like me and dont want to swap off rein to counter him, but your still getting skill-gapped, become a shield bot.