From what I've seen in the areas you're looking there isn't much available that's already setup as a multi unit where the numbers will work. If you're willing to flex on location a little there's quite a few options zoned correctly where you can convert the garage or add an ADU. I also wanted to be in the areas you described and looked for 3 years. Someone advised me to expand my search area and I'm glad I did.
East Oakland is currently working on the the Rapid Transit line which should bring eventual growth to the area. For $389k I bought a 1200 sq. ft 2 bedroom in the area (that can easily be converted to a 3 bdrm) with a standalone 2 car garage I will convert. When the project is finished it will either work as a house hack or I can rent out both and it will cash flow. I didn't have to deal with inherited tenants and I can set rent to current market rate. I was able to do a conventional loan with 10% down. I was surprised at how easily I found financing by saving just a little more down, working with an agent who specialized in class B & C properties, and shopping around.
You will want to look into zoning for the area you buy in ahead of time, but currently things seem relaxed due to the housing shortage. Of course all this assumes you're willing to do the leg work and deal with construction projects. But for the total cost you're looking to spend you could shift areas, buy something for less, funnel the difference into rehabbing, and come out much more on top long term.