Only direct communication with the credit card provider can answer this for sure. Get it in writing or record the call if you're serious.
How they work:
Nearly all rewards cards decide to honor our not honor a reward based on MCC code numbers (Merchant Category Codes). Every credit card "terminal" is assigned a code between 0000 and 9999 (from a list that is co-maintained by the IRS and Visa/Mastercard) when it is first set up and that code seldom changes. (It doesn't matter what you buy)
"Rewards card" credit card programs create groups of MCC Code numbers that they usually call categories.
MCC# 4900 is utilities for example.
MCC# 0742 is veterinatian services.
US Bank's CashPlus has a user selectable 5% category called "Utilities" that is just MCC code 4900.
Amalgamated Bank of Chicago has a quarterly category called "Health Services" category that includes 0742 as well as the codes used by most hospitals and doctor's offices.
BBVA's ClearPoints Rewards card offers a category called "Retail" which is pretty choice. It's almost all brick and mortar stores. But Grocery, Restaurats, Autoparts&service & gas are excluded.
It's rare but not unheard of for a credit-card-program-defined category to include a specific named store, like walmart.com online. I've even seen some that honor all transactions processed through apple-pay or google-pay. But I've never seen one that subtracts a specific store from otherwise qualifying by its MCC code.
I don't have a BofA card, but you should call your service rep and ask them to "specifically list each of the four digit numerical MCC category code numbers that apply" to the categories you're curious about. Transfer to another rep until you find one who understands what you're asking.
the Visa Supplier locator will let you look up MCC numbers of physical stores. https://www.visa.com/supplierlocator/index.jsp
The USDA for some reason is hosting a big list of the codes and their descriptions: https://www.dm.usda.gov/procurement/card/card_x/mcc.pdf
Notice the description text is often listed verbatim in the credit card company's category descriptions.
To sum it up:
It's misleading to think that "online purchases" has anything to do with "anything paid for online".
"Online Purchases" is merely what BofA calls a group of qualifiers (typically mcc codes).
The way you pay (online or in store) is kind of immaterial.
Source: This is my primary sport. I earn points every month on over a dozen cards, with about 3 dozen rewards cards open and available. All paid off weekly. I earn between $200-300 in points monthly.