Will I still be able to manage QBO files through Banks Feeds after my Desktop Pro 2021 goes out of support?

The potential problem is the bank feed feature after May 2024. You can download .qbo files from your bank BUT you can't import directly into your QB Desktop. If your bank provides *.csv files, you will need to use a 3rd party tool to import it into QB Desktop. It's a $199 one time license and you can get $100 cashback to purchase the license from a partner.
https://get.transactionpro.com/qbd

Thanks for letting us know about your queries, ITGuys. I can provide input to help you in managing QuickBooks Desktop data.

With QBDT's discontinuation policy, services affected by this notice won't receive live access to technical support, critical security patches and updates, and other Intuit programs that integrate with the product after May 31, 2024. 

That said, utilizing the bank feeds features and managing transactions you'll manually import to the desktop data will entirely be affected once the QBDT 2021 program goes out of support. After the discontinuation date, you're unable to complete these tasks.

You may want to check out this guide for more detailed information: QuickBooks Desktop service discontinuation policy.

If you want to consider upgrading your desktop program to the latest version, you may continue utilizing our add-on services efficiently.

Furthermore, I'm sharing these references to help you secure a backup copy of your company file and learn more about what's new with the latest version of QBDT:

• Back up your QuickBooks Desktop company file.
• What’s new in QuickBooks Desktop 2024.

I'll keep this thread available, so you can always get back to us whenever you require additional assistance managing your QuickBooks data. I'll be around anytime you need further help. Stay safe and have a good one!

RE: Will I still have the ability to utilize the Bank Feeds function within QB Desktop Pro and manage transactions that I import manually using downloaded QBO files?

You won't be able to import *.QBO files.

RE: Additionally, I import my externally managed payroll via an IIF file. I don't see anything mentioned about losing import functionality, so I'm hoping I can continue to import those IIF files also.

You will be able to import IIF files as usual.

As you're used to using IIF files, you may find our BRC OFX/QFX/QBO to IIF Converter helpful. You can use it to convert QBO files into IIF files and then import the IIF files.