This is not vendor activity: "I have a situation where an employee used a personal card for some business expenses and many personal expense.  I am using a suspense account for the amounts the firm paid towards that credit card."

The Firm never pays anyone's personal credit card, directly. You reimburse the employee under the terms of An Accountable Plan. They pay their own Bills and costs.

"I was planning to Journal Entry  Credit Card Payments Suspense - Credit / Proper Expense Account for Expense - Debit.  The idea is that anything left over in the Credit Card Payments Suspense after JE all business expenses is compensation to that employee. (Another JE to zero out the Suspense account)."

It's not Compensation to the employee under the terms of An Accountable Plan. And you would not be Overpaying, ever.

"But using JEs this way in QBO is not showing as a payment to the vendor  under vendors lookup for the reason  youl explained.  So I wonder, is there a QBO way to accomplish what I am after?"

You told us this is an Employee. That means Not your credit card to track or pay.

I just provided an answer to a similar topic:

There are these 2 things:

1. Business resources were used to Buy something. It is was already paid, or will be paid alter, because the supplier is willing to let you Pay Later = Accounts Payable.

2. Personal resources were used to Buy something. That means it is Already Paid For. That means we either need to enter the Owner Paid using personal resources. Or, we need to reimburse an employee.

You start with How paid: now or later, and By Whom. And the business entity type matters.

To reimburse an employee for "lots of things" you can simply issue a Check. Or, to add it to the direct deposit paycheck, you do it like this:

Make a Bank account and name it Payroll Clearing. Enter here the Spending for each employee. The Employee is the Payee name. Do this for that date of payroll, not the Purchased dates. Enter your actual details, accounts, products, services, job tracking, billable, etc, in the expense transactions.

Now you have a Bank account running negative for this Paydate.

Make a Payroll net pay addition that is linked to this bank account and set for no tax tracking, as long as what you reimburse for is do under An Accountable Plan. Following those rules make this Not really part of payroll and not taxable; just a banking addition. Add this same amount to that employee's check.

That acts as a Deposit to the Payroll Clearing Bank. That bank should now show 0 balance for the pay date, if you did this right. And now you also captured the spending details.

Avoid using AP and Vendors, for employee reimbursement. They are Already Employees, not also running a separate business as your vendor, and you need to show this reimbursement process meets the requirements of An Accountable Plan, or Doesn't meet that requirement and is taxable through payroll.