Is it possible for a third party app to access macOS's clipboard content? I am asking in relation to copy & paste sensitive data such as passwords and sensitive file content.
No security for data that is in one of the system clipboards is possible by design.
The macOS clipboard is a public billboard open to all processes. Clipboard is the mechanism to let all apps read / modify shared data.
Either restrict your set of apps installed to those you trust with the data or don't ever copy sensitive content into the clipboard for your least trustworthy app.
From here, the rabbit hole for developers and security minded people using macOS begins with an overview of secure text input options within programs to prevent key loggers in addition to pasteboard snoopers from grabbing secure input:
Any process with sufficient permissions can read your clipboard at any time, and you can't easily prevent this. Security is always a trade-off with usability, and this is the choice that most (but not all) OSes take when implementing the clipboard.
Some apps that store sensitive data (e.g. 1Password) implement a timeout such that any information you copy out of that application is cleared from the clipboard a short time later. If you'd like to do something like that globally, you could look at the answers to this previous question for ideas.