Your "handy men" are idiots. I suggest you give no credence to them in the future, even if they are related. The white wire is the neutral wire. Black is hot. Bare wire is ground.

Yes...please do not let these 'handymen" anywhere near your house.

"but most of the ones I’m interested in buying require a neutral wire..."

Outlets will always have a neutral wire as noted above. You can't power anything without both a hot and a neutral wire. The problem is with switches; many (most?) don't have a neutral wire so that will limit what you can install to control lights and/or outlets.

Describe what you are trying to achieve. That may result in more help.

Outlets will always have a hot (usually black, sometimes red) and a neutral (white).

Switches will always have a hot, but may or may not have a neutral. If the switch is on a ”switch leg”, it will not have a neutral. If a switch is connected to a black and a white (the white might have black tape/paint/marker on it), then the switch is probably on a ”switch leg”.

”Smart switches” will usually require a neutral and, often, are hard/impossible to use on a ”switch leg”.

Sometimes you can buy ”smart switches” that are battery powered and communicate wirelessly with the target outlet/device.

All of your photos seem to be of an electrical outlet. You are more likely to have a problem with a switch (due to possibly not having a neutral) than with an outlet.

Maybe post photos of some switches you would like to replace. It might be possible to tell if the switch has a neutral. I would trust an electrician to give the right answer vs a handyman.