I can help you record the government payment in QuickBooks Online (QBO), srmcmahon.

To record this, you'll have to create an expense account specifically for recording the reimbursement. Then, make a vendor credit and apply it to the expense. Doing so will ensure accurate tracking of the reimbursement and the related expenses in QBO.

Here's how:

1. Go to the Transactions menu or Gear icon.
2. Select Chart of Accounts.
3. Click the New button.
   
4. Tap Expenses.
5. In the Save account under drop-down arrow, choose Expenses.
6. Choose the Tax form section from the drop-down arrow.
7. Enter the account name.
8. Hit Save.
   

Once done, create a vendor credit. I'll guide you on how to do it.

1. Go to the +New button.
2. Select Vendor credit.
   
3. Choose the government agency as the vendor.
4. Enter the reimbursement amount as a negative value. 
5. In the Category column, select the expense account you created.
6. Press Save and close.
   

After that, apply it to the expense.

1. Go to the +New button.
2. Click Expense.
3. Choose the private vendor from whom you purchased the ergonomic equipment as the payee.
4. Enter the amount of the reimbursement as a positive value. 
5. In the Category column, select the expense account associated with the purchase of ergonomic equipment.
6. Tap Save and Close.
   

I'd also suggest seeking guidance from your accountant to help you choose the right account.

I hope this explanation helps. If you have any further questions or concerns, please let me know. I'm more than willing to help. Take care!