I don't usually reply on these types of threads, but for some reason, here we go...
Background: Former military pilot, current 121 Captain. I've got some failed checkrides in my past and while I HATE going to the sims, I don't think I have any unusual anxiety about checkrides... Here's my free advice with a money back guarantee. It's now on the internet so it must be right.
1. Be a good FO. In addition to and knowing your duties, don't forget to pay attention to what the captain is doing. Whenever they are making a decision, decide in your mind what (and why) you would have done. If they do something different, instead of talking about CBA issues, COVID vaccines, and all the other useless time fillers, try asking the captain for their thought process when making the decision. You may or may not end up agreeing, but it can really expand your horizons on what considerations may matter when you change seats. Also, pay attention to their leadership styles. What works and what doesn't. You mentioned that you're the quiet type. The loud overbearing leadership style is actually not usually the best one to facilitate CRM. Use examples from folks you fly with to build yours so you can empower your FO's to be assets to you. And maybe do little things like remind you of max bank angles while you are finishing a previous checklist.
2.Checkrides (and other training events). We've all flown with folks that say to keep your mouth shut so you don't dime yourself out to an examiner. I've never believed that. The check airman has nothing better to do than notice every single little thing you screw up. If they hear you mumbling to yourself that you just got off altitude and see you were correcting, do you think that'll go better than if they have no idea if you even knew you screwed up? Do your best to forget that they're back there, fly the best airplane (not sim) that you can, identify and fix the inevitable mistakes that WILL happen, and let the chips fall where they will. If you are mentally engaged in flying, not wasting your time trying to evaluate your own ride, you'll be calmer and make better decisions.
3. Unless you're at a company that forces you to upgrade, realize that 121 flying is NOT like the military. No one is looking down at you or critizing you for "lack of career progression" if you don't upgrade "on time." Sit back as an FO, learn your job, pay attention to the captain, and upgrade when you're ready. For me, I knew I was ready when I kinda knew what most captains were going to do or say before they did, and knew when captains were forgetting things or considerations that I could help with. On the flip side, don't sit in the right seat until you get lazy from doing it in your sleep forever.
Just my thoughts...