What is the strategy that works for you to budget for Rosh hashana and sukkos?

I love this question! My recommendation would be to take the large known costs and divide amongst the year and create a fund for it. If you spend 120 on an esrog, put 10 dollars away a month (ynab makes this easy) so the money is there when you need it.

Sometimes especially for yomim tovim there are unknown and unexpected costs. I’m curious to know ways that have worked for people to deal with those as well.

The strategy shouldn't change based on how expensive things are. You only have the money that you have. You can put away more throughout the year, or find cheaper ways to do it, but the one thing that is fixed is how much you have at the time you buy it. There also shouldn't really be unexpected costs, maybe the first 2-3 years you end up with costs you didn't expect due to lack of experience, but after that what could happen that causes an unexpected cost to pop up? If there really are unexpected costs (maybe the sukkah was destroyed 2 weeks before sukkos due to flooding). Thats what an emergency fund is for.

I think I could give lots of examples of unexpected costs (especially when "unexpected" in terms of an annually amortized amount could mean even a change 3 months in advance), but at the end of the day the answer stays the same, which is estimate and have an emergency fund.

Using an emergency fund for Yom Tov could be devastating. Yom Tov is not an emergency - you know exactly when it's coming, it never changes- and if you mentally think it's okay to draw from your emergency fund for that, then next time it'll be something much more mundane. Also, that means you'll have to be replenishing your emergency fund AND saving up for the next Yom Tov at the same time, and I don't know how practical that is for most people. I know expenses can change, which is why it's so so important to have our spouses on board.

Using an emergency fund for Yom Tov could be devastating. Yom Tov is not an emergency

To clarify my point above. Yom Tov is not an emergency, but if there are expenses that are unexpected, that would constitute an emergency. As a general rule the expenses should be predictable though.

I'm curious what you would consider unexpected Yom Tov expenses that would justify dipping into the emergency fund?

The area your sukkah is in floods and the sukkah boards are ruined and you need to buy a new one,

Your esrogs pitom falls off

Esrog just means one less piece of meat, you don't need to buy a $100 Esrog if you haven't budgeted for it. The second is better, but that kind of means you don't have a Yom Tov fund at all since you were going to your parents, so in that case they'd technically be the same fund.

I said above that I could give a long list of examples but I don't think it's a fruitful exercise. But for one example that happened to someone I know - they bought their yom tov food (meat and fish and whatever else for all of the seudos) and then the freezer somehow got left open without being noticed for something like 2 days (freezer was in the basement) and all the meat/fish was no good. I can come up with lots of examples...

I agree with @witty-engineer-80805 that you can do all the budgeting you want and hashem can still flip everything on its head