Does the program automatically recover passive loss carryover on the sale of rental property or must I do so manually?

It depends. If you report the sale in the Rental & Royalty Income (SCH E) section of the program, then those carry over losses are "usually" dealt with just fine by the program, including depreciation recapture. But if in any one year the rental was active you had a situation with carry overs the program was not able to handle, then you'll have to enter those losses manually.

Go ahead and report the sale in the SCH E section of the program (Guidance provided below) and when done review IRS forms 8582 and 4797.

Reporting the Sale of Rental Property

If you qualify for the "lived in 2 of last 5 years" capital gains exclusion, then when prompted you WILL indicate that this sale DOES INCLUDE the sale of your main home. For AD MIL personnel who don't qualify because of PCS orders, select this option anyway, because you "MIGHT" qualify for at last a partial exclusion.

Start working through Rental & Royalty Income (SCH E) "AS IF" you did not sell the property. One of the screens near the start will have a selection on it for "I sold or otherwise disposed of this property in  2019". Select it. After you select the "I sold or otherwise disposed of this property in 2019" you continue working it through "as if" you still own it. When you come to the summary screen you will enter all of your rental income and expenses, even it it's zero. Then you MUST work through the "Sale of Assets/Depreciation" section. You must work through each individual asset one at a time to report its disposition (in your case, all your rental assets were sold).

Understand that if more than the property itself is listed in your assets list, then you need to allocate your sales price across all of your assets.  You will only allocate the structure sales price; you will NOT allocate the land sales price, since the land is not a depreciable asset.  Then if you sold this rental at a gain, you must show a gain on all assets, even if that gain is $1. Likewise, if you sold at a loss then you must show a loss on all assets, even if that loss is $1

Basically, when working through an asset you select the option for "I stopped using this asset in 2019" and go from there. Note that you MUST do this for EACH AND EVERY asset listed.

When you finish working through everything listed in the assets section, if you ever at any time you owned this rental you claimed vehicle expenses, then you must also work through the vehicle section and show the disposition of the vehicle. Most likely, your vehicle disposition will be "removed for personal use", as I seriously doubt you sold your vehicle as a part of this rental sale.

In the introductory part of the rental section (where you enter the general information, such as the address), check that it sold, and that the sale was a "fully taxable transaction".  That will release the Passive Loss Carryover.