You are hovering too much for sure.
water, walk away.. it's okay to inspect it but stop convincing yourself you have to do "something" to quel your purely internal anxiety.
Always water the whole substrate, this is never "overwatering." If issues arise from that simple behaviour it is due to a poorly constituted substrate. for any typical soil you want 50% perlite or similar drainage amendment. for coco coir you only need 33% because it holds proportionally less water per volume.
A humidity dome early on is not for the seedling. It ensures you won't have to water again until well after it sprouts. You can remove the dome after it sprouts, too. Even if you use a tiny seedling pot, it will retain moisture for 4-5 days, which is plenty of time for a seed to sprout without having to water a 2nd time before the roots are out.
You have a tiny plant in a big pot. This makes watering difficult. In this istuations, you water a 3-4" diameter around where the seed will be planted and make sure that column of moisture goes all the way down to the bottom, or you did it wrong. Half-watering is always setting yourself up for failure down the line. Always water to the bottom and a little runoff ensures that occured.
Wait for top 1" to dry, and repeat. For a seedling in a small pot, You may want to pre-empt that slightly, but still wait for top to start to dry.
A little algea, which is probably the green you see, is no big deal but a sign that the soil remained wet for far too long. This can happen in normal situations too. Once the canopy is fuller and you have a plant wiht some roots, a proper wet-dry cycle and lack of light will quickly kill off any algea that accumulated. Algea is superficial only. Not optimal for a sprout, but usually won't kill a sprout either. If algea is surviving, then other microbes that can cause "damping off" are a risk too. Correlates but doesn't cause.
less is more.. if you are fiddling or digging or prodding.. stop it. Treat it like a 2nd child. Do what is needed and stop doing what makes you feel good.
use smaller pots for seedlings - something that will last 7-10 days. Use more aeration amendments in soil. Track how long it takes to sprout and adjust depth of planting accordingly. Getting nearly all of them to sprout within 3 days is a good goal. If in a cold climate, a heating pad with thermostat is a useful tool to increase consistency of sprout times. simply press down with a finger - forms a good base. drop seed in. loosely cover from side and gently tamp down. Fastest sprout without a helmet head (seed shell stuck) is the depth and pressure you want to apply when planting. One-time learning curve.
Water.. check on them each day but don't do anything else until transplant or dry enough to warrant a watering... you water based on how much the plant drinks and not some premeditated schedule in your head. observe and react... don't try to dictate to the plant. (except for training / shaping plant)