Since your MacBook Neo had this problem before macOS Golden Gate 27, appeared to improve after updating, and is now exhibiting the same behaviour, I'd first establish exactly what is happening and whether macOS detects the expected update.
Open System Settings → General → Software Update and note whether the check completes, continues indefinitely, or reports that your Mac is up to date. Under Apple menu → About This Mac, confirm your installed macOS version.
You previously had to download and install an update manually. How did you download and install it, and which troubleshooting steps have you already tried? This will help avoid repeating them.
To check whether macOS lists available updates independently of the Software Update window, open Terminal and run:
softwareupdate --list
This command checks for available updates without installing them. Please share the complete output, including any errors. If Terminal lists the expected update but System Settings does not, that helps narrow down the problem; if it lists no updates, the cause remains undetermined.
Please also provide the Apple webpage listing the update you expect, including its version number if available. An update listed on Apple's website is not necessarily offered to every Mac in every configuration, so comparing the exact update with your installed version and Terminal results will help clarify the situation.
Depending on the findings, consult Apple's macOS update troubleshooting guidance.
