hi marlinam
welcome to this Apple (user-to-user) Community!
Re: "Voice Control does not work in a lot of app text fields, instead of showing a small red icon. This had occurred somewhat in a previous version of macOS, but since upgrading to macOS sequoia 5.3.1, even more text fields seem to be newly blocked (e.g. Protonmail on Firefox), without explanation or recourse. Can anyone explain?"
Seems Apple integrates accessibility features into much of it's software, however not all third-party (non-Apple) apps and software developers have the skills, inclination, (or time and money) to do the same.
Articles online, such as Web Content Accessibility Guidelines (WCAG) 2.1 are available for web-developers,
Eg; says:
"Following these guidelines will also often make Web content more usable to users in general".
Guidelines are available for app-developrs and those in other fields too,but not all may get to use them.
Of course, Apple is quite separate from many other companies involved in producing apps, web-content, etc.
The control and responsibility of the accessibility level of software development rests with the company who makes it.
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Re; "And is there anything I can do to change it? It is a real hindrance to accessibility which is very good with voice control when it works. I would ideally like voice control to work in all text fields."
I guess Voice Control etc. works wherever it is supported by software producers / administrators.
Perhaps you can send feedback to the manufacturers, suppliers, or development teams, support departments or such, of any third-party products, software etc. you come across that are not as accessible as desired.
In some cases, developers / designers may already be trying to make their products more accessible.
Eg: For Apple: To provide feedback about an accessibility feature on an Apple product,
You can email the Accessibility team: accessibility@apple.com