The Social Security Administration (SSA) has a great tool called the "Accessible Name & Description Inspector", or "ANDI" for short. To use this tool, you need to run it on a page you wish to test and then examine each element on the page to make sure that what you see visually and what is presented programmatically are the same. Some parts of the page, such as blocks of text, won't be shown with ANDI as those are pretty accessible as is.
ANDI has several screens, but all work in a very similar way. In the following screenshot, you can see that we are on the "focusable elements" tool. On the far left are forward and back buttons that allow you to move through all the focusable elements on the page. The next column shows information about the current element, such as what kind of element it is and any accessibility features enabled on it, etc.
At the bottom of this column is "ANDI Output" which is the information that a screen reader will be presented. This is the main bit of information that you want to pay attention to with this tool as this is roughly the same as what a screen reader will present when focused on this element.
For comparison, here is the structures tool showing the same missing Heading that was found with our accessibility checking tools above. There isn't an error flagged per say, but note that the output is cryptic message of "heading level 2" and not something that would provide information for a user to navigate the page.
Note that in addition to focusable elements and structures as outlined above, numerous other tools will appear, some of which are dependent on the content on the page. On the tested page, the following options were present when running ANDI.