To me, failure is the the result of an action which causes stress.

That sounds wrong I guess, because you assume that you can have stressful situations where you succeed. But more correctly I mean that when you make that internalized evaluation of whether you should do something or not, you look back on your experience doing that thing, and remember whether it caused you stress or if it made you motivated. Even if the process is stressful, if the end result is more enjoyable than stressful, it's a success. Otherwise a failure.

Failure is a pretty key part of learning and building habits. Things that you have attempted and failed are going to drum of feelings of stress and anxiety when you contemplate attempting them again. Things that you have attempted and succeeded at are going to bring feelings of motivation when you think about doing them.

I don't know that changing what failure means to you affects a lot, but I definitely think that for me, understanding how stress plays into my willingness to continue trying to do something makes a big difference. For instance, when you allow yourself to be really hard on yourself for an interstitial failure, (like making a schedule to work out 3 times a week and missing a day) it makes you feel a bit more stressed the next time you consider attempting it... it gets harder. Eventually you decide it's too hard to keep trying if you're just going to fail, and you give up (often you attribute this to personal failings). But if you want to get in the habit of going to the gym 3 times per week, the best way to do it is to go to the gym 3 times per week. Missing a day shouldn't cause stress, nor should missing a month. You shouldn't feel "failure", because the "success" condition should be the results of going to the gym regularly, not some artificial construction of maintaining a schedule. And in that respect, you're not failing, you're just not achieving that success condition as quickly as possible.

When you base your internalized feelings of success or failure around external constructs like that, you kind of undermine your actual learning and habit forming systems. Is your goal really to be fit? Because the goal you are really working towards is forcing a routine. The achievement of some abstract goal (checking off all the attendance boxes for an undefined length of time) instead of a more organic goal (actually feeling healthier).

I used the workout schedule as an example because it's an example where the end result makes you feel good on it's own. But I think this idea can be used in business too. Failure should be something you feel in situations that you want to avoid in the future, but you need to be careful not to feel too much failure for situations you want to improve. If you associate the whole action as a failure, you'll just have more difficulty attempting it in the future, improving.

I have pretty good control over how I deal with stress, but I struggle with how to organize my priorities. The goal is to do my best and only let myself feel stress when it's absolutely necessary, or when I'm in a situation that if I fail, I should avoid trying it again.

Some people use stress to force themselves into action, because it's a strong motivator. These people tend to dislike many things. Failure comes frequently to them, and just the idea of failure causes stress and anxiety, which fuels them further. It's one way to handle things, and I used to deal with things this way, but I think it's less healthy, and less controllable.

In conclusion, Failure is an abstract up condition made up to cause stress for not meeting an abstract goal. They are methods we use to affect our internal decision and habit forming processes. Success is an abstract reward for meeting a goal that may not have it's own intrinsically rewarding qualities. Failure is an abstract stressor for not meeting that goal that may not have it's own intrinsically painful qualities. If we understand how we are, individually, affected by stress and reward, we can structure how and when we let ourselves feel failure to help stop demotivating us from our real objectives.

For me, rarely letting myself feel like I've failed has reduced my day to day stress, which makes it a lot easier to control myself emotionally. That was a hard thing to let go of though. However, if I need to try to motivate myself, setting goals with a success condition and no failure condition seems to work better. I started doing Judo a few months ago, the instructor had to leave town and I didn't jive with the new instructor as much, and I hurt myself and decided to stop going to the class. Some people would feel like they failed by not following through with that. If another class with a different instructor were to start up they might feel less inclined to sign up because they already tried to do that and failed. But I only remember how I enjoyed the class, and would look forward to doing it again if I could enjoy it the same way.