Startup costs & Depreciation for guest house

Your rental income/expenses is reported on SCH E. You begin reporting in the tax year the property is "available for rent"; meaning the first day it's ready for an occupant. So if it was available for rent in Dec 2021 you report it on SCH E. It does not matter if you actually had a paying renter in there or not.

I didn't deduct those start-up costs on our 2021 return.

Start-up costs are not deductible for rental property reported on SCH E. They never have been. However, if you qualify as a SCH C business things are handled a bit differently. It is not easy for residential rental real estate to qualify as a SCH C business, even if it's for short term rental through AirB&B or VRBO. For one thing, you have to provide substantial services that are directly beneficial to the tenant, and that does not include services performed between tenants. For a gist that is not all inclusive, see https://ttlc.intuit.com/turbotax-support/en-us/help-article/form-1040/report-rental-schedule-e-schedule-c/L2rrDNcI3_US_en_US

Should I amend our 2021 1040?

Only if the property was available for rent on or before Dec 31 of 2021.

Also, is it advised or necessary to depreciate the building?

Depreciation starts on the day the property is available for rent. While there's nothing in writing that says you "have" to depreciate the property, you are higly advised to do so. When you later sell or otherwise dispose of the property, you are required by law to recapture the depreciation and pay taxes on it in the tax year you close on the sale. If you do not depreciate the property, then you are still required to recapture and pay taxes on the depreciation you "should" have taken. Two things happen with depreciation recapture.

1) The recaptured depreciation is added to your AGI in the tax year you sell and you will pay taxes on it.

2) Depending on the numbers, recapture depreciation can bump your AGI into the next higher tax bracket. Weather it does or not just depends on the numbers.

I see no place in the mortgage paperwork that specifies the portion of costs for building(s) versus land, and our property tax assessor lists the ADU as a separate "improvement", valued in a way that is an advantage to us for property taxes but will not be if I extrapolate it to its original cost.

Tax values are never used for depreciation. Depreciation is based on the "LESSER" of the FMV on the date you converted it to a rental, or your original acquisition cost when you originally purchased the property; whichever is "lower".  It is not common for the value of the property to be less than what you originally paid for it. So more than likely you will use the original purchase price.

You use the tax bill only to figure percentages of your acquisition cost to assign to the structure and the land.  The tax assessor will typically value your property for property taxes only, and not based on its fair market value (FMV) Example:

Tax bill says your land is valued at $30,000, your primary residence is valued at $70,000 and the ADU (Additional Dwelling Unit) is valued at $20,000. So the total tax value of the property is $120,000

You paid $200,000 for the property when you originally purchased it back in 2010.

Of the $120,000 tax value, 25% is for the land, 58.3% is for your primary residence, and the remaining 16.7% is for the ADU.

Of the $200,000 original purchase price, you paid 16.7% of that for the ADU, which is $33,400.  Then you can figure roughly the percentage of the land allocated to the ADI with a "best guess". I would guess around 30%.

With the tax bill showing the land value as 25% of the total tax value, that makes 25% of your $200,000 original purchase price at $50,000 for the land. If we allocate 30% of the land to the ADU, that gives a land value of $15,000

So for this rental, your "COST" will be $48,400 and "Cost of Land" would be $15,000.

The program (not you) will do the math to figure the cost basis of the ADU to be $33,400 and that amount will be used to figure depreciation over the next 27.5 years.

If you qualify as a SCH C business (which I doubt, but can't rule out the possibility) then depreciation would be over 39 years.