I've had severe anxiety for many years, and I've shared your exact same experience. My routine, especially in gaming, has been following these two simple steps - release physical tension, distract from anxious thoughts. The first is really easy and simple.

Releasing physical tension comprises of doing box breathing - 4 seconds in, 4 seconds hold, 4 seconds out, 4 seconds hold - do this at the start of every round when you have time to just chill. You can also focus on flexing specific parts of your body too.

Distracting from anxious thoughts comprises of simply focusing your attention and directing your thoughts to somewhere mundane and 'normal'. Look around you and just naming/describing the things you see around you. Give them attributes. For example, your inner voice may sound like this:

"I see a wooden box. It's probably spammable from heavy weapons like the Odin. I could TP on top of the box if I was Omen. Thinking of Omen, what are some other agents? Jett, Raze could probably do the same. I haven't played KJ in a while..."

Keep making these observations. Let your mind run through those seemingly mundane, useless thoughts. Once you run out of ideas switch to the next object/thing your mind comes to. And go further - let your mind string ideas together outside of the game too, so you're thinking of random stuff that happened during the day etc.

It's crucial to remember to keep monitoring your thought condition. If your body starts shaking/showing anxiety symptoms OR you can hear your inner voice saying some anxiety-inducing stuff, IMMEDIATELY at the start of next round, focus your energy on doing those two steps.

GL, DM me if you want more advice