I think you’re missing the balancing that needs to happen that’s internal to each party’s books. That’s where an expense account would come in, using the accounting equation:

               ∆ State = ∆ Change
                       ↓ 
  Assets - Liabilities = Income - Expense

For example you had:

> 3. The employee submitting their expense report (invoice) to the company for reimbursement (liability to the company, asset to the employee)

So looking just at the company’s books:

  $0 Asset - $100 Liability = $0 Income - $100 Expense
                -$100 State = -$100 Change

Then in step 4: > The employee getting paid by the company for the incurred expense (company converts asset into a discharge of liability, employee converting receivable into cash)

The company’s books would be:

  -$100 Asset + $100 Liability = $0 Income - $0 Expense
                      $0 State = $0 Change

So the net impact on the ledger would be (putting these entries together):

  -$100 Asset - $100 Liability + $100 Liability = $0 Income - $100 Expense
                     -$100 Asset - $0 Liability = $0 Income - $100 Expense
                                    -$100 State = -$100 Change

Which is exactly what the company’s books would have recorded if they were using cash accounting instead of accrual. They spent $100 on an Expense.

So I think it’s super important to make a distinction between Liability and Expense Accounts because they’re on different sides of the accounting equation - State and Change. The same distinction applies to Asset and Income Accounts. [1]

[1] https://fragment.dev/docs#design-your-ledger-ledger-accounts