I have big anxiety problems too, but I actually prefer Series than Open. So I'm the opposite perspective here, but I'll share & see if it can be useful.
Only gaining 8pts (I'm S rank) for every win & always losing 4pts for every loss regardless of the badges I get in Open is actually an utter TORTURE to me. I'm not a sigma grindset squid. I don't wanna sink THAT much time on Splatoon even if I love Splatoon. My left hand's fingers could use more lifetime. They've started hurting easier ever since I dipped my hands into competitive.
I don't wanna lose my thumb cartilage from Splatooning too hard like Ookami Mio did, lol:
I play Open when I don't feel confident going straight into Series yet & wanna warm up with less points risk, or if I just wanna brain empty & play TC/SZ and Open happens to have it while Series doesn't.
It sometimes depends on the players online too - it can sometimes feel like I was meeting more questionable teammates in one mode or the other.
Series is a gamble, but if I can perform at least average, I can get even a little bit more points than in Open. If I can perform great, then that's even better! I get a TON of points and that feels great to have my silver & gold badges amounting to something.
If I'm not doing so hot, then I can stop or play Open to repay a bit of my loss before calling it a day, or review my replays while I snack and chill, etc.
Simply put, Open is my testing/lazing ground, Series is my real business hours.
As for tilting, it happens no matter whether it's in Series or Open for me.
Mindset-wise, I like to detach myself a bit and think "go next, nothing I can do about it now". Then a moment later, I'd mentally review what went wrong & what I could've done better.
Usually I have a narrative video/stream playing while gaming so that I have something to get my mind off the tension & remind myself to take it easy, take a breather, don't get carried away with what has passed, regard the last game as if I've shaken hands with the players and reset my mind for the next game. Or stop for awhile if I feel too tilted and don't see my performance getting better. Then I can either attempt again, review my replays or call it a day.