"Are these the 3 pieces if I am actually processing a payroll for the purpose of just adding the value of the personal use of company vehicle?"

That business (whose 2022 return is likely going to need to be amended) would already have all operating expense tracked. What you are missing is the other two: Gross (grossed up if necessary) taxable additional (typically monthly, quarterly, or at least year end) and then the Net (valued) deduction (to avoid paying it out as money).

As noted, the issues include, when this is paid by itself (resulting in a net $0 check), this is treated as supplemental wages (subject to higher income tax flat withholding rate 22% or more, even). Also, not included with regular pay means nothing to deduct from. If there is no more pay to give the person, there is nothing from which to deduct the employee share of Soc Sec and Medicare, so that is when you Gross Up, and that would be treated as loan to employee, to be repaid as net pay deduction out of one or more later paychecks. Examples:

Paycheck Gross $5,000

Vehicle value benefit $1,000 (gross addition as taxable fringe)

Taxed on gross $6,000 (let's pretend that comes to $1,779)

Deduct any after-tax values, include $1,000 for fringe benefit = $3,221 takehome

Now you see how $1,000 benefit value (cost to the employer) is offset by the $1,000 pay deduction, which you might see like this:

Vehicle expenses for this operating year $23,500

less vehicle expense recaptured -$1,000

QB won't do this for you. Someone needs to value the benefit and figure out how to handle deductions.

I found a great article for you for reference:

https://www.patriotsoftware.com/blog/payroll/personal-use-company-vehicle-car-tax-pucc/

"without me actually processing a payroll."

Example:

Vehicle benefit $1,000 = Gross pay $1,000

Let's pretend withholdings total $300. But, Net Deduction needs to be that same amount of $1,000. You will need a (not taxable) addition of Loan to Employee $300, to be repaid by payroll deduction later.

Or, you need to keep doing the math to gross up the $1,000 value so that the total paid out matches the total deducted after withholding. That means the gross taxable is something around $1422, but split into Fringe Benefit $1,000 and then a wage/bonus of $422.

If it is part of payroll, it impacts 941/944, 940, SUTA, etc.

Fringe Benefit paychecks end at $0, because the employee already got that value in the benefit.

I hope that helps.