What happens in this case?

I’m going to assume the answer is the option where the insurance company gets the most money, but I want to ask anyway.

Tldr mini example:

Allergy testing goes towards my deductible, which I’ve barely filled in 2023. I have a date set for December 22nd 2023 to do the testing. Will the dare of service make it apply to my 2023 deductible instead of 2024? If so, is there any way to make sure it applies to 2024 instead? How does that work?

More in-depth catastrophe example I guess:

Let’s say you need some type of surgery on the day of December 31st, and it costs so much it fulfills your entire deductible – would this fall under 2023, so that your entire 2023 deductible is suddenly fulfilled and then the next day it’s completely reset?

Also curious in the case that your hospital stay goes into the first week of January for example. Is it possible in any way to get the costs from December 31st rolled into the 2024 deductible? I’m not sure if it’s dependent on date of service, or when the bill is received (or if it varies by company??)

And let’s say your deductible is $5k. Does this example mean that you’d be paying $10k total since your hospital stay and services went from 2023-2024?

Thank you to anyone who can answer this, all I see on google is “it depends”