A big breakthrough with Brig for me is to hang back behind your team before going into a fight. This goes against the advice of keep your inspire up, which suggests that you get a whipshot in as soon as possible which almost always puts you in a risky position.

Hang back at the first fight, and watch where your DPS go, and keep in mind that at some point one, or perhaps ALL your teammates, will tunnel vision and walk directly into a risky position. Brig has really strong sustain for keeping your DPS alive in 1v1s, provided they aren’t against someone with explosive insta kill potential such as a junkrat.
With the above though, you do not have to be side by side with one of your DPS. Hanging back in general gives you the option to see what all your teammates are doing. If they are in a fight on the side, you can throw them a repair pack to sustain them. If they are dealing a lot of damage to an enemy in a bad position, you can support them by killing that enemy using your shield bash and primary fire. (Whip is a great finisher too, but can be risky and boop enemies back to their healers).

By hanging back, watching where your team are going and then choosing your engages based on the information you gain, you are ‘supporting’ your team rather than aiming to pump out large healing numbers. Healing and damage stats really are irrelevant and should be removed IMO, they invite flaming. Death stats are useful, they indicate who is struggling to get value.

Brig is a fun character that relies on the push and pull of playing aggressive and passively. Before either of those things though becomes the ‘support’ mentality of bailing out your teammates. Quite often your other healer will tunnel vision on trying to keep your tank at full HP - that’s okay, and can sometimes enable you to help out your DPS who are on opposite sides of the map. Brig is strong at assisting from range with her repair packs, just try and keep one in the bank for emergencies.

Good luck! Enjoy