Where do I locate the 'tax liability' amount for the section that says, "Tell Us About Your 2022 Oregon Return"? I don't remember having a Form OR-40 so I'm confused

Yes, the form OR-40 is quite different from the W-2. 

Form OR-40 is the page 1 of the Oregon tax return (like 1040 is for the federal return).

The W-2 is, of course, what your employer gives you as a record of your wages.

Your W-2 is the document your employer issues to you and to the IRS to show how much you were paid and how much tax was withheld from your pay.

https://turbotax.intuit.com/tax-tips/irs-tax-forms/what-is-a-w-2-form/L6VJbqWl5

Your OR-40 is the state tax return form you prepared for the state and sent to the state to seek a tax refund from the state.  It will be in your online account for 2022.

  You have to access your own account and/or  print it for yourself using exactly the same account and user ID that you used when you prepared the return.

Start a 2023 return online and enter some personal information  so that the menu on the left opens up and lets you access your past year returns.

https://ttlc.intuit.com/community/prior-year-return/help/how-do-i-access-my-prior-year-return/01/27010

Many people have multiple TT accounts and forget how to access them.  Log out of the account you are in now.

Account Recovery

https://ttlc.intuit.com/questions/1901535-forgot-your-turbotax-online-user-id-or-password

Or did you use the desktop version of TurboTax?  If so, the files are on your own hard drive or any backup device you used like a flash drive.

https://ttlc.intuit.com/questions/1901486-how-many-turbotax-accounts-do-i-have

https://ttlc.intuit.com/questions/1901659-find-your-tax-data-file-in-mac

https://ttlc.intuit.com/questions/1900721-find-your-tax-data-file-tax-file-in-windows

You can get a free transcript from the IRS or for a fee of $43, an actual copy of your tax return.

https://www.irs.gov/individuals/get-transcript

https://www.irs.gov/pub/irs-pdf/f4506.pdf

SAVE YOUR TAX RETURN !

EVERY year before mid-October you should save a copy of your tax return as a pdf and print a copy of it for your records.  That way you will not be searching online frantically when you need it for a lender, FAFSA forms, your next tax return, etc. 

https://ttlc.intuit.com/questions/1900937-why-should-i-save-a-pdf-copy-of-my-return

https://ttlc.intuit.com/questions/1899779-what-s-the-difference-between-the-tax-data-file-and-the-pdf-file

https://ttlc.intuit.com/questions/1912466-how-do-i-save-my-return-as-a-pdf-in-the-turbotax-software-for-windows •

NOTE:  TurboTax and the IRS save returns for seven years.  Returns older than seven years are purged.

I want to know that same answer.  form OR-40 doesn't say "Oregon Tax Liability" on it anywhere.

It could vary based on why you are asking, but Oregon's tax liability is probably line 20 on the OR-40. Note that the answer might also vary if you are not a full-time resident so using a different form.