Those are not real screws. You can find several images onlines on how it comes apart, like this: https://poshmark.com/listing/Apple-Watch-gold-metal-case-63b8d998ffb5d0b96ff9b1f2

Just use google reverse image search for more information.

It’s more like a physics problem than a software problem. Imagine if Apple decreses the sensitivity on wrist detection to make the Apple watch experience better for tattoed users, so they decide to ignore some instances when the light emitted by the sensors can’t provide enough feedback because they are absorbed by the dark spots. That would overall make the safety features of the watch worse, for example in theory someone could just snatch the watch off you on the street, then fasten it on their own wrist and carry on with it, using ApplePay and such… so overall it’s a difficult problem to handle, it’s no wonder Apple still could not address it after releasing 9 generations of watches. It’s not because they are lazy to release a simple software patch. You can influence them to maybe shift priorities and work on this issue more by submitting your feedback, that’s about all you can do right now unless you are willing to remove or lighten the tattoo.

Almost everyone with tattoos has experienced this issue, probably you have already seen the hundreds of posts about it for the past 7 years, but the severity of the problem with wrist detection varies based on the darkness, technique, age, etc. of the tattoo. If your previous watches cooperated better, then it’s probably because the sensors on the back of the Ultra are situated a bit differently, (same circular layout, but not the same) so now the sensors are being blocked more by the pattern on your wrist. Also, the Ultra is heavier than previous models, so based on how you hold your hand during the workout, if the band is not tight enough, the watch body may slightly shift away from your skin instead of laying flat, making things worse. In any case, the optical sensors on the Ultra in this regard were not made better or worse for tattoo users. Auto-pausing the workout is not what happens to you, that’s a separate feature you can disable in settings under workout. Your workout tracking fails because wrist detection fails.

Try wearing different bands, try wearing your watch further up or down your wrist or switch hands if that’s possible for you.