when should I replace or upgrade an old appliance?

If you need it to work, and it does not work, and you cannot fix it.
If you have multiple years of money saved up, and it is taxing something besides money, and opening up will allow you to achieve something worthwhile.
If you have tons of money and you just do not want to do it.

There's levels to this.

First level is survival mode. Scrimp, survive. Day to day. Maybe a week, not a month.

Second level is saving mode. Scrimp, survive, save. Week to week, month to month, not a year.

Third level is well once you figure out saving mode, I guess money flows or investing mode, business mode. Sustainability mode. Solving the money problem by creating a sustainable source or sources of income coupled with spending habits that are lower.

Fourth level is enjoyment mode? I do not know. That is further than I can see, but I see people saying they just spend for convienience. Money is no longer an issue.

Fifth level, well I think we are moving beyond money now to like, enjoyment, contentment, and that is where these things start to come together. Maybe people try to have legacy with money, but the thing is legacy comes from other things. It is kind of like how at some point, you need to do something else. Happiness. And happiness is not money, but the lack of can be related. Kind of like, going from no safe living area to a safe living area to a nice house. Well, those are huge. But at some point, you will get diminishing returns. Spending on a nicer and nicer and nicer or more houses will not get you the level of happiness increase as the other levels did.

When is something broken?
Depends on your ability to fix it, have it fixed, deal with it not working.

What should you prioritize?
Things that impact health, education, experiences with friends and family, safety. Same kind of priorities. Ability to earn money.

Also consider how often you use something and for what purpose.

If it is often and the purpose is important, then consider that item.

What are guidelines?
When it does not work, you cannot fix it, and you cannot pay to have it fixed, or it is not worth it. Ex. spend a weekend fiddling with something when a replacement is $2 for 50 of them, and they last years each. That is an extreme example.

When it works, but it is limping along? That is the best time and position to be in for looking for deals. How do you know something is limping along? When a reasonable person cannot just go and just use it. Like you have to do something special to turn it on, or it is precarious conditions in order for it to work. A bodged solution that does not quite work well.

When the cost to replacement is going to go up or there is a really good sale. These things change. Right now there is a glut of production for large appliances and the dollar is continuing to inflate. The purchasing power is going down, down, down. Eventually these home appliances will have to be replaced. They are important to function. You can get something new and nice and functional. But normally they are so expensive.

But right now? Prices getting slashed for sales. And they will cost more or be lower quality in the future.

Go for it.