The items you discussed are separate from an emergency fund concept.
The whole article could be one paragraph.
Put about 90% of your emergency fund in a money market (mine earns 4.6%). These are same as cash.
Keep the rest in a savings account.
Use the savings account for small emergencies.
Use the money market if you, for example, lose your job.

I keep 50K in a money market and 5K in savings.
Invest the rest of your portfolio.