I cleared all the website data and logged back in again, then tried to make a test post but the same thing happened.

I don't know what it is exactly, but I think I've worked out what it's related to. The reason I changed to Safari was because it allows you to create isolated web apps, meaning that you can run websites more like their own independent app rather than a webpage in your browser. Many browsers allow you to do this, but most of them aren't isolated. This means that any cookies and trackers you download from the web apps are still linked to your normal browser. However, Safari web apps are totally isolated, so you can create a web app for Facebook for example and the trackers Facebook uses are 'trapped' (isolated) inside your Facebook web app, and can't be cross referenced with your normal browser.

I created a web app for CEO, so my Mac now sees it as an app, rather than a browser, hence when I click on the '?', it talks about 'apps' needing to access my keychain, not a browser (even though a browser is still an app, but you know what I mean...)

I tried inputting my password for the CEO site and it refused it, meaning that it wants the password for my whole system, ie, my entire keychain. I'm sure there's nothing nefarious about CEO but I'm still not happy giving it my system password, especially when it doesn't seem to ask for this when I use other web apps which I have to log into, such as Facebook.

Anyway, I've gone back to just using CEO in my normal browser, and the problem has gone.

Yes, the password for Keychain is your device/system password, not the website password.
It’s a component of OS & Safari.

I personally would just enable it. But I’m also pretty limited in what I access, too.