My first reaction is my experience and observation that yield-chasing is generally a horrible investment strategy. Dividends are paid by companies with no compelling use for their cash flow. They can't expand. Can't invest in new tech. Can't grow. So they slow-motion liquidate through dividends. Some are so bad as to pay dividends while also paying high interest on a growing pile of debt.
My second reaction is that if you lost your job or had to downsize your earnings, earning 5-6% on - what? - $30k or $40k is not going to move the needle much. Sure, a couple of grand per year helps, but it won't keep you from being homeless if you can't work. Plus there's the time it takes to amass this fund.
Assuming you have zero debt, here are what I think are better ideas to become more resilient to potential job loss, in no particular order:
1) Get a roommate: This pays at least several thousand a year. Maybe more in HCOL areas. This can also be the easiest option.
2) Lower your housing expenses: Buying a small, basic house in a LCOL area is often half the monthly payment as a rented apartment. Save up a down payment. This also makes #1 easier.
3) Lower your transportation expenses: You could have a very nice bike within a few months of saving spare money. Or pay for a move closer to work.
4) Invest in efficiency: If you own your home, insulation, storm windows, a newer fridge, or a new air conditioner could yield a competitive ROI.
5) Consider if you have landlord potential: You could save up a down payment on a rent house or duplex in a LCOL area. Some people get 10-20 properties and FIRE with very little equity. Just make sure the numbers work (in my city they don't).
6) Get certifications: These can make you more employable AND increase your income. E.g. a technical certification and a project management certification would go well with that MBA, but so would a healthcare certification and some legal training. Accounting is a good area to dive into when you're already in the banking industry.
7) Preventative maintenance: Bald tires, rusty plumbing, dust-clogged computers, worn out roofing, and HVAC systems that have never been cleaned/recharged are accidents waiting to happen. This is where $1 investment can save $10.