Should I include the bills I owe in the ‘medical expenses’ from last year, if I plan on paying them this year? or should I wait until next year when they’re paid off?

No, only include expenses you actually paid for in 2023.  Anything you pay for this year (in 2024) goes on next year's return.   

You can only deduct what you actually paid each year.  If you put it on a credit card or took out a loan you can deduct the full amount even though you pay it over time. If you are on a payment plan with the hospital or doctor, etc. then it's only the amount you pay. Either way you only can deduct the principal amount, not any interest.

I'm not following you about planning to pay them off this year, etc.  For 2023 only what you actually paid.  

And then you can only deduct the amount of unreimbursed Medical Expenses you actually paid over 7.5% of your AGI. So it might take a lot to be worth entering. And then all your itemized deductions have to be more than the standard deduction to get any benefit (so you would only be getting the benefit of the amount that puts you over the standard deduction). And since the Standard Deduction is increased more people will not need to Itemize.

For 2023 the standard deduction amounts are:

Single 13,850 + 1,850 for 65 and over or blind (15,700)

HOH 20,800 + 1,850 for 65 and over or blind (22,650)

Joint 27,700 + 1,500 for each 65 and over or blind (29,200/30,700)

Married filing Separate 13,850 + 1,500 for 65 and over or blind (15,350)