QB Issue Resolution:

In cash basis reporting for sales, COGS is only posted when the sale is paid
that assumes you have paid for the inventory purchase

You said,¬†In my old desktop version, I could run a monthly report and see how much it cost me to purchase the products I sold that month. In the online version, the only things that show up in cost of goods sold are products I’ve paid for that month, whether I have sold them or not.

IF you are using inventory type items, then the purchase cost does NOT show in COGS (cash or accrual) until the item sold.  If it has been showing in cogs, then either you have the inventory item set up wrong, or you are recording the purchase incorrectly

Inventory  items have three accounts
expense = COGS
income = your sales income account
asset = inventory asset

See this for a How To Receive Inventory Items. (desktop)
http://onsale-apparel.com/Rustler/tag/how2-rcv-inven

though this link explains desktop, the concept is the same in QBO except you use the item details part of a purchase instead of the item tab which is shown.

you do have to turn on that item details part for some strange reason, in company settings>expenses>bills & expenses turn on the items table and purchase orders

Resolution for Issue 'How can I get the Cost of Goods sold to show up in monthly profit/loss reports? If I do a quarterly p&l it will show up, but not monthly.' available: Yes (Solved).
Source: Intuit Community forum.

How can I get the Cost of Goods sold to show up in monthly profit/loss reports? If I do a quarterly p&l it will show up, but not monthly.: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

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